 8.8.4.1: In Exercises 1 to 12, use mathematical induction to prove each stat...
 8.8.5.1: In Exercises 1 to 8, evaluate the binomial coefficient.74b
 8.8.1.1: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.1: In Exercises 1 to 10, evaluate each quantity. P(6, 2)
 8.8.2.1: In Exercises 1 to 14, find the 9th, 24th, and nth terms of the arit...
 8.8.7.1: In Exercises 1 to 10, list the elements in the sample space defined...
 8.8.3.1: In Exercises 1 to 20, find the nth term of the geometric sequence. ...
 8.1: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.2: In Exercises 1 to 12, use mathematical induction to prove each stat...
 8.8.5.2: In Exercises 1 to 8, evaluate the binomial coefficient.a b 86
 8.8.1.2: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.2: In Exercises 1 to 10, evaluate each quantity. P(8, 7)
 8.8.2.2: In Exercises 1 to 14, find the 9th, 24th, and nth terms of the arit...
 8.8.7.2: In Exercises 1 to 10, list the elements in the sample space defined...
 8.8.3.2: In Exercises 1 to 20, find the nth term of the geometric sequence. ...
 8.2: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.3: In Exercises 1 to 12, use mathematical induction to prove each stat...
 8.8.5.3: In Exercises 1 to 8, evaluate the binomial coefficient.92
 8.8.1.3: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.3: In Exercises 1 to 10, evaluate each quantity. C(8, 4)
 8.8.2.3: In Exercises 1 to 14, find the 9th, 24th, and nth terms of the arit...
 8.8.7.3: In Exercises 1 to 10, list the elements in the sample space defined...
 8.8.3.3: In Exercises 1 to 20, find the nth term of the geometric sequence. ...
 8.3: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.4: In Exercises 1 to 12, use mathematical induction to prove each stat...
 8.8.5.4: In Exercises 1 to 8, evaluate the binomial coefficient.a105
 8.8.1.4: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.4: In Exercises 1 to 10, evaluate each quantity. C(9, 2)
 8.8.2.4: In Exercises 1 to 14, find the 9th, 24th, and nth terms of the arit...
 8.8.7.4: In Exercises 1 to 10, list the elements in the sample space defined...
 8.8.3.4: In Exercises 1 to 20, find the nth term of the geometric sequence. ...
 8.4: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.5: In Exercises 1 to 12, use mathematical induction to prove each stat...
 8.8.5.5: In Exercises 1 to 8, evaluate the binomial coefficient.129
 8.8.1.5: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.5: In Exercises 1 to 10, evaluate each quantity. P(8, 0)
 8.8.2.5: In Exercises 1 to 14, find the 9th, 24th, and nth terms of the arit...
 8.8.7.5: In Exercises 1 to 10, list the elements in the sample space defined...
 8.8.3.5: In Exercises 1 to 20, find the nth term of the geometric sequence. ...
 8.5: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.6: In Exercises 1 to 12, use mathematical induction to prove each stat...
 8.8.5.6: In Exercises 1 to 8, evaluate the binomial coefficient.a b 65
 8.8.1.6: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.6: In Exercises 1 to 10, evaluate each quantity. P(9, 9)
 8.8.2.6: In Exercises 1 to 14, find the 9th, 24th, and nth terms of the arit...
 8.8.7.6: In Exercises 1 to 10, list the elements in the sample space defined...
 8.8.3.6: In Exercises 1 to 20, find the nth term of the geometric sequence.8...
 8.6: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.7: In Exercises 1 to 12, use mathematical induction to prove each stat...
 8.8.5.7: In Exercises 1 to 8, evaluate the binomial coefficient.110
 8.8.1.7: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.7: In Exercises 1 to 10, evaluate each quantity. C(7, 7)
 8.8.2.7: In Exercises 1 to 14, find the 9th, 24th, and nth terms of the arit...
 8.8.7.7: In Exercises 1 to 10, list the elements in the sample space defined...
 8.8.3.7: In Exercises 1 to 20, find the nth term of the geometric sequence....
 8.7: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.8: In Exercises 1 to 12, use mathematical induction to prove each stat...
 8.8.5.8: In Exercises 1 to 8, evaluate the binomial coefficient.1414
 8.8.1.8: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.8: In Exercises 1 to 10, evaluate each quantity. C(6, 0)
 8.8.2.8: In Exercises 1 to 14, find the 9th, 24th, and nth terms of the arit...
 8.8.7.8: In Exercises 1 to 10, list the elements in the sample space defined...
 8.8.3.8: In Exercises 1 to 20, find the nth term of the geometric sequence....
 8.8: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.9: In Exercises 1 to 12, use mathematical induction to prove each stat...
 8.8.5.9: In Exercises 9 to 32, expand the binomial. (x + y)5
 8.8.1.9: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.9: In Exercises 1 to 10, evaluate each quantity. C(10, 4)
 8.8.2.9: In Exercises 1 to 14, find the 9th, 24th, and nth terms of the arit...
 8.8.7.9: In Exercises 1 to 10, list the elements in the sample space defined...
 8.8.3.9: In Exercises 1 to 20, find the nth term of the geometric sequence.9...
 8.9: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.10: In Exercises 1 to 12, use mathematical induction to prove each stat...
 8.8.5.10: In Exercises 9 to 32, expand the binomial. (x + y)7
 8.8.1.10: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.10: In Exercises 1 to 10, evaluate each quantity. P(10, 4)
 8.8.2.10: In Exercises 1 to 14, find the 9th, 24th, and nth terms of the arit...
 8.8.7.10: In Exercises 1 to 10, list the elements in the sample space defined...
 8.8.3.10: In Exercises 1 to 20, find the nth term of the geometric sequence.8...
 8.10: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.11: In Exercises 1 to 12, use mathematical induction to prove each stat...
 8.8.5.11: In Exercises 9 to 32, expand the binomial. (a  b)4
 8.8.1.11: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.11: Computer Systems A computer manufacturer offers a computer system w...
 8.8.2.11: In Exercises 1 to 14, find the 9th, 24th, and nth terms of the arit...
 8.8.7.11: In Exercises 11 to 15, use the sample space defined by the experime...
 8.8.3.11: In Exercises 1 to 20, find the nth term of the geometric sequence.1...
 8.11: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.12: In Exercises 1 to 12, use mathematical induction to prove each stat...
 8.8.5.12: In Exercises 9 to 32, expand the binomial. (a  b)6
 8.8.1.12: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.12: Color Monitors A computer monitor produces color by blending colors...
 8.8.2.12: In Exercises 1 to 14, find the 9th, 24th, and nth terms of the arit...
 8.8.7.12: In Exercises 11 to 15, use the sample space defined by the experime...
 8.8.3.12: In Exercises 1 to 20, find the nth term of the geometric sequence.2...
 8.12: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.13: In Exercises 13 to 20, use mathematical induction to prove each ine...
 8.8.5.13: In Exercises 9 to 32, expand the binomial. (x + 5)4
 8.8.1.13: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.13: Computer Science A fourdigit binary number is a sequence of four d...
 8.8.2.13: In Exercises 1 to 14, find the 9th, 24th, and nth terms of the arit...
 8.8.7.13: In Exercises 11 to 15, use the sample space defined by the experime...
 8.8.3.13: In Exercises 1 to 20, find the nth term of the geometric sequence.c...
 8.13: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.14: In Exercises 13 to 20, use mathematical induction to prove each ine...
 8.8.5.14: In Exercises 9 to 32, expand the binomial. (x + 2)6
 8.8.1.14: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.14: Computer Memory An integer is stored in a computers memory as a ser...
 8.8.2.14: In Exercises 1 to 14, find the 9th, 24th, and nth terms of the arit...
 8.8.7.14: In Exercises 11 to 15, use the sample space defined by the experime...
 8.8.3.14: In Exercises 1 to 20, find the nth term of the geometric sequence....
 8.14: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.15: In Exercises 13 to 20, use mathematical induction to prove each ine...
 8.8.5.15: In Exercises 9 to 32, expand the binomial. (a  3)5
 8.8.1.15: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.15: Scheduling In how many different ways can six employees be assigned...
 8.8.2.15: In Exercises 15 to 18, find the requested term. The fourth and fift...
 8.8.7.15: In Exercises 11 to 15, use the sample space defined by the experime...
 8.8.3.15: In Exercises 1 to 20, find the nth term of the geometric sequence.3...
 8.15: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.16: In Exercises 13 to 20, use mathematical induction to prove each ine...
 8.8.5.16: In Exercises 9 to 32, expand the binomial. (a  2)7
 8.8.1.16: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.16: Contest Winners First, second, and thirdplace prizes are to be a...
 8.8.2.16: In Exercises 15 to 18, find the requested term. The sixth and eight...
 8.8.7.16: In Exercises 16 to 20, use the sample space defined by the experime...
 8.8.3.16: In Exercises 1 to 20, find the nth term of the geometric sequence.7...
 8.16: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.17: In Exercises 13 to 20, use mathematical induction to prove each ine...
 8.8.5.17: In Exercises 9 to 32, expand the binomial. 2x  1)7
 8.8.1.17: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.17: Mailboxes There are five mailboxes outside a post office. In how ma...
 8.8.2.17: In Exercises 15 to 18, find the requested term. The fifth and seven...
 8.8.7.17: In Exercises 16 to 20, use the sample space defined by the experime...
 8.8.3.17: In Exercises 1 to 20, find the nth term of the geometric sequence.0...
 8.17: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.18: In Exercises 13 to 20, use mathematical induction to prove each ine...
 8.8.5.18: In Exercises 9 to 32, expand the binomial. (2x + y)6
 8.8.1.18: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.18: Committee Membership How many different committees of three people ...
 8.8.2.18: In Exercises 15 to 18, find the requested term. The fourth and seve...
 8.8.7.18: In Exercises 16 to 20, use the sample space defined by the experime...
 8.8.3.18: In Exercises 1 to 20, find the nth term of the geometric sequence.0...
 8.18: In Exercises 1 to 18, find the third and seventh terms of the seque...
 8.8.4.19: In Exercises 13 to 20, use mathematical induction to prove each ine...
 8.8.5.19: In Exercises 9 to 32, expand the binomial. (x + 3y)6
 8.8.1.19: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.19: Test Questions A professor provides to a class 25 possible essay qu...
 8.8.2.19: In Exercises 19 to 32, find the nth partial sum of the arithmetic s...
 8.8.7.19: In Exercises 16 to 20, use the sample space defined by the experime...
 8.8.3.19: In Exercises 1 to 20, find the nth term of the geometric sequence.0...
 8.19: In Exercises 19 to 26, evaluate the expression. 5! + 3!
 8.8.4.20: In Exercises 13 to 20, use mathematical induction to prove each ine...
 8.8.5.20: In Exercises 9 to 32, expand the binomial. (x  4y)5
 8.8.1.20: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.20: Tennis Matches Twentysix people enter a tennis tournament. How man...
 8.8.2.20: In Exercises 19 to 32, find the nth partial sum of the arithmetic s...
 8.8.7.20: In Exercises 16 to 20, use the sample space defined by the experime...
 8.8.3.20: In Exercises 1 to 20, find the nth term of the geometric sequence.0...
 8.20: In Exercises 19 to 26, evaluate the expression. 6!  5!
 8.8.4.21: In Exercises 21 to 30, use mathematical induction to prove each sta...
 8.8.5.21: In Exercises 9 to 32, expand the binomial. (2x  5y)4
 8.8.1.21: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.21: Employee Initials A company has more than 676 employees. Explain wh...
 8.8.2.21: In Exercises 19 to 32, find the nth partial sum of the arithmetic s...
 8.8.7.21: Playing Cards From a standard deck of playing cards, one card is ch...
 8.8.3.21: In Exercises 21 to 24, find the requested term of the geometric seq...
 8.21: In Exercises 19 to 26, evaluate the expression. 10!6!
 8.8.4.22: In Exercises 21 to 30, use mathematical induction to prove each sta...
 8.8.5.22: In Exercises 9 to 32, expand the binomial. (3x + 2y)4
 8.8.1.22: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.22: Seating Arrangements A car holds six passengers, three in the front...
 8.8.2.22: In Exercises 19 to 32, find the nth partial sum of the arithmetic s...
 8.8.7.22: Tossing Coins A coin is tossed four times. Find the probability of ...
 8.8.3.22: In Exercises 21 to 24, find the requested term of the geometric seq...
 8.22: In Exercises 19 to 26, evaluate the expression. 3! # 4!
 8.8.4.23: In Exercises 21 to 30, use mathematical induction to prove each sta...
 8.8.5.23: In Exercises 9 to 32, expand the binomial. (x2  4)7
 8.8.1.23: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.23: Committee Membership A committee of six people is chosen from six s...
 8.8.2.23: In Exercises 19 to 32, find the nth partial sum of the arithmetic s...
 8.8.7.23: Tossing Coins A coin is tossed four times. Find the probability of ...
 8.8.3.23: In Exercises 21 to 24, find the requested term of the geometric seq...
 8.23: In Exercises 19 to 26, evaluate the expression. a b 123 b
 8.8.4.24: In Exercises 21 to 30, use mathematical induction to prove each sta...
 8.8.5.24: In Exercises 9 to 32, expand the binomial. (x  y3)6
 8.8.1.24: In Exercises 1 to 24, find the first three terms and the n eighth t...
 8.8.6.24: Arranging Numbers The numbers 1, 2, 3, 4, 5, and 6 are to be arrang...
 8.8.2.24: In Exercises 19 to 32, find the nth partial sum of the arithmetic s...
 8.8.7.24: Playing Cards One card is drawn from a standard deck of playing car...
 8.8.3.24: In Exercises 21 to 24, find the requested term of the geometric seq...
 8.24: In Exercises 19 to 26, evaluate the expression. a158 a b
 8.8.4.25: In Exercises 21 to 30, use mathematical induction to prove each sta...
 8.8.5.25: In Exercises 9 to 32, expand the binomial. (2x2 + y3)5
 8.8.1.25: In Exercises 25 to 34, find the first three terms of each recursive...
 8.8.6.25: Test Questions A truefalse examination contains 10 questions. In ho...
 8.8.2.25: In Exercises 19 to 32, find the nth partial sum of the arithmetic s...
 8.8.7.25: Number Theory Let Twodigit natural numbers less than 100 , and con...
 8.8.3.25: In Exercises 25 to 36, determine whether the sequence is arithmetic...
 8.25: In Exercises 19 to 26, evaluate the expression. 5k=1k 2
 8.8.4.26: In Exercises 21 to 30, use mathematical induction to prove each sta...
 8.8.5.26: In Exercises 9 to 32, expand the binomial. (2x  y3)6
 8.8.1.26: In Exercises 25 to 34, find the first three terms of each recursive...
 8.8.6.26: Test Questions A 20 question, fouroption multiplechoice examinati...
 8.8.2.26: In Exercises 19 to 32, find the nth partial sum of the arithmetic s...
 8.8.7.26: Playing Cards One card is drawn from a standard deck of playing car...
 8.8.3.26: In Exercises 25 to 36, determine whether the sequence is arithmetic...
 8.26: In Exercises 19 to 26, evaluate the expression. 6j=11a j!
 8.8.4.27: In Exercises 21 to 30, use mathematical induction to prove each sta...
 8.8.5.27: In Exercises 9 to 32, expand the binomial. (x + 1y)5
 8.8.1.27: In Exercises 25 to 34, find the first three terms of each recursive...
 8.8.6.27: State Lottery A state lottery game requires a person to select 6 di...
 8.8.2.27: In Exercises 19 to 32, find the nth partial sum of the arithmetic s...
 8.8.7.27: Number Theory Let Natural numbers less than or equal to 100 , and c...
 8.8.3.27: In Exercises 25 to 36, determine whether the sequence is arithmetic...
 8.27: In Exercises 27 to 34, find the requested term or partial sum for t...
 8.8.4.28: In Exercises 21 to 30, use mathematical induction to prove each sta...
 8.8.5.28: In Exercises 9 to 32, expand the binomial. (2x  1y)7
 8.8.1.28: In Exercises 25 to 34, find the first three terms of each recursive...
 8.8.6.28: Test Questions A student must answer 8 of 10 questions on an exam. ...
 8.8.2.28: In Exercises 19 to 32, find the nth partial sum of the arithmetic s...
 8.8.7.28: Number Theory A single number is chosen from the digits 1, 2, 3, 4,...
 8.8.3.28: In Exercises 25 to 36, determine whether the sequence is arithmetic...
 8.28: In Exercises 27 to 34, find the requested term or partial sum for t...
 8.8.4.29: In Exercises 21 to 30, use mathematical induction to prove each sta...
 8.8.5.29: In Exercises 9 to 32, expand the binomial. a2x  x2b4
 8.8.1.29: In Exercises 25 to 34, find the first three terms of each recursive...
 8.8.6.29: Acceptance Sampling A warehouse receives a shipment of 10 computers...
 8.8.2.29: In Exercises 19 to 32, find the nth partial sum of the arithmetic s...
 8.8.7.29: Economics An economist predicts that the probability of an increase...
 8.8.3.29: In Exercises 25 to 36, determine whether the sequence is arithmetic...
 8.29: In Exercises 27 to 34, find the requested term or partial sum for t...
 8.8.4.30: In Exercises 21 to 30, use mathematical induction to prove each sta...
 8.8.5.30: In Exercises 9 to 32, expand the binomial. aab+bab
 8.8.1.30: In Exercises 25 to 34, find the first three terms of each recursive...
 8.8.6.30: Contest Fifteen students, of whom seven are seniors, are selected a...
 8.8.2.30: In Exercises 19 to 32, find the nth partial sum of the arithmetic s...
 8.8.7.30: Number Theory Four digits are selected from the digits 1, 2, 3, and...
 8.8.3.30: In Exercises 25 to 36, determine whether the sequence is arithmetic...
 8.30: In Exercises 27 to 34, find the requested term or partial sum for t...
 8.8.4.31: In Exercises 31 to 35, use mathematical induction to prove each sta...
 8.8.5.31: In Exercises 9 to 32, expand the binomial. (s2 + s2)6
 8.8.1.31: In Exercises 25 to 34, find the first three terms of each recursive...
 8.8.6.31: Serial Numbers A television manufacturer uses a code for the serial...
 8.8.2.31: In Exercises 19 to 32, find the nth partial sum of the arithmetic s...
 8.8.7.31: Building Industry An owner of a construction company has bid for th...
 8.8.3.31: In Exercises 25 to 36, determine whether the sequence is arithmetic...
 8.31: In Exercises 27 to 34, find the requested term or partial sum for t...
 8.8.4.32: In Exercises 31 to 35, use mathematical induction to prove each sta...
 8.8.5.32: In Exercises 9 to 32, expand the binomial. (2r1 + s1)5
 8.8.1.32: In Exercises 25 to 34, find the first three terms of each recursive...
 8.8.6.32: Playing Cards Five cards are chosen at random from a standard deck ...
 8.8.2.32: In Exercises 19 to 32, find the nth partial sum of the arithmetic s...
 8.8.7.32: Acceptance Sampling A shipment of 10 calculators contains 2 defecti...
 8.8.3.32: In Exercises 25 to 36, determine whether the sequence is arithmetic...
 8.32: In Exercises 27 to 34, find the requested term or partial sum for t...
 8.33: In Exercises 27 to 34, find the requested term or partial sum for t...
 8.8.4.33: In Exercises 31 to 35, use mathematical induction to prove each sta...
 8.8.5.33: In Exercises 33 to 40, find the indicated term without expanding. (...
 8.8.1.33: In Exercises 25 to 34, find the first three terms of each recursive...
 8.8.6.33: Acceptance Sampling A quality control inspector receives a shipment...
 8.8.2.33: In Exercises 33 to 36, insert k arithmetic means between the given ...
 8.8.7.33: Number Theory Five random digits are selected from 0 to 9 with repl...
 8.8.3.33: In Exercises 25 to 36, determine whether the sequence is arithmetic...
 8.34: In Exercises 27 to 34, find the requested term or partial sum for t...
 8.8.4.34: In Exercises 31 to 35, use mathematical induction to prove each sta...
 8.8.5.34: In Exercises 33 to 40, find the indicated term without expanding. (...
 8.8.1.34: In Exercises 25 to 34, find the first three terms of each recursive...
 8.8.6.34: Basketball Teams A basketball team has 12 members. In how many ways...
 8.8.2.34: In Exercises 33 to 36, insert k arithmetic means between the given ...
 8.8.7.34: Queuing Theory Six people are arranged in a line. What is the proba...
 8.8.3.34: In Exercises 25 to 36, determine whether the sequence is arithmetic...
 8.35: In Exercises 35 and 36, insert the arithmetic means. Insert 4 arith...
 8.8.4.35: In Exercises 31 to 35, use mathematical induction to prove each sta...
 8.8.5.35: In Exercises 33 to 40, find the indicated term without expanding. (...
 8.8.1.35: In Exercises 35 and 36, find a3, a4, and a5. a1 = 1, a2 = 3, an = 1...
 8.8.6.35: Arranging Numbers The numbers 1, 2, 3, 4, 5, and 6 are arranged ran...
 8.8.2.35: In Exercises 33 to 36, insert k arithmetic means between the given ...
 8.8.7.35: Lottery A box contains 500 envelopes, of which 50 have $100 in cash...
 8.8.3.35: In Exercises 25 to 36, determine whether the sequence is arithmetic...
 8.36: In Exercises 35 and 36, insert the arithmetic means. Insert 5 arith...
 8.8.4.36: Steps in a Proof by Mathematical Induction In every proof by mathem...
 8.8.5.36: In Exercises 33 to 40, find the indicated term without expanding. (...
 8.8.1.36: In Exercises 35 and 36, find a3, a4, and a5. a1 = 1, a2 = 4, an = (...
 8.8.6.36: Occupancy identical balls are randomly put in seven containers so t...
 8.8.2.36: In Exercises 33 to 36, insert k arithmetic means between the given ...
 8.8.7.36: Jury Selection A jury of 12 people is selected from 30 people: 15 w...
 8.8.3.36: In Exercises 25 to 36, determine whether the sequence is arithmetic...
 8.37: In Exercises 37 to 44, find the requested term or sum for the geome...
 8.8.5.37: In Exercises 33 to 40, find the indicated term without expanding. (...
 8.8.1.37: Lucas Sequence The Lucas sequence is similar to the Fibonacci seque...
 8.8.6.37: Lines in a Plane Seven points lie in a plane in such a way that no ...
 8.8.2.37: Show that the sum of the first n positive odd integers is n2.
 8.8.7.37: Queuing Theory Three girls and three boys are randomly placed in si...
 8.8.3.37: In Exercises 37 to 46, find the sum of the finite geometric series....
 8.38: In Exercises 37 to 44, find the requested term or sum for the geome...
 8.8.5.38: In Exercises 33 to 40, find the indicated term without expanding. (...
 8.8.1.38: RATS Sequence RATS stands for Reverse, Add, T hen Sort. The first f...
 8.8.6.38: Chess Matches A chess tournament has 12 participants. How many game...
 8.8.2.38: Show that the sum of the first n positive even integers is n2 + n.
 8.8.7.38: Committee Membership A committee of four is chosen from three accou...
 8.8.3.38: In Exercises 37 to 46, find the sum of the finite geometric series....
 8.39: In Exercises 37 to 44, find the requested term or sum for the geome...
 8.8.5.39: In Exercises 33 to 40, find the indicated term without expanding. a...
 8.8.1.39: In Exercises 39 to 46, evaluate the factorial expression. 7!  6!
 8.8.6.39: Contest Winners Eight couples attend a benefit dinner at which two ...
 8.8.2.39: Stacking Logs Logs are stacked so that there are 25 logs in the bot...
 8.8.7.39: Extrasensory Perception A magician claims to be able to read minds....
 8.8.3.39: In Exercises 37 to 46, find the sum of the finite geometric series....
 8.40: In Exercises 37 to 44, find the requested term or sum for the geome...
 8.8.5.40: In Exercises 33 to 40, find the indicated term without expanding. a...
 8.8.1.40: In Exercises 39 to 46, evaluate the factorial expression. (4!)2
 8.8.6.40: Geometry Suppose there are 12 distinct points on a circle. How many...
 8.8.2.40: Theater Seating The seating section in a theater has 27 seats in th...
 8.8.7.40: Playing Cards One card is randomly drawn from a standard deck of pl...
 8.8.3.40: In Exercises 37 to 46, find the sum of the finite geometric series....
 8.41: In Exercises 37 to 44, find the requested term or sum for the geome...
 8.8.5.41: In Exercises 41 to 48, find the requested term. Find the term that ...
 8.8.1.41: In Exercises 39 to 46, evaluate the factorial expression. 9!7!
 8.8.6.41: Test Questions In how many ways can a student answer a 20 question...
 8.8.2.41: Contest Prizes A contest offers 15 prizes. The 1st prize is $5000, ...
 8.8.7.41: Scheduling A meeting is scheduled by randomly choosing a weekday an...
 8.8.3.41: In Exercises 37 to 46, find the sum of the finite geometric series....
 8.42: In Exercises 37 to 44, find the requested term or sum for the geome...
 8.8.5.42: In Exercises 41 to 48, find the requested term. Find the term that ...
 8.8.1.42: In Exercises 39 to 46, evaluate the factorial expression. 10!5!
 8.8.6.42: Committee Membership From a group of 15 people, a committee of 8 is...
 8.8.2.42: Physical Fitness An exercise program calls for walking 15 minutes e...
 8.8.7.42: National Defense A missile radar detection system consists of two r...
 8.8.3.42: In Exercises 37 to 46, find the sum of the finite geometric series....
 8.43: In Exercises 37 to 44, find the requested term or sum for the geome...
 8.8.5.43: In Exercises 41 to 48, find the requested term. Find the term that ...
 8.8.1.43: In Exercises 39 to 46, evaluate the factorial expression. 8!3! 5!
 8.8.6.43: Committee Membership From a group of 20 people, a committee of 12 i...
 8.8.2.43: Physics An object dropped from a cliff will fall 16 feet the first ...
 8.8.7.43: Oil Industry An oil drilling venture involves drilling four wells i...
 8.8.3.43: In Exercises 37 to 46, find the sum of the finite geometric series....
 8.44: In Exercises 37 to 44, find the requested term or sum for the geome...
 8.8.5.44: In Exercises 41 to 48, find the requested term. Find the term that ...
 8.8.1.44: In Exercises 39 to 46, evaluate the factorial expression.12!4! 8!
 8.8.6.44: Checkerboards A checkerboard consists of eight rows and eight colum...
 8.8.2.44: Physics The distance a ball rolls down a ramp each second is given ...
 8.8.7.44: Manufacturing A manufacturer of CDROMs claims that only 1 of every...
 8.8.3.44: In Exercises 37 to 46, find the sum of the finite geometric series....
 8.45: In Exercises 45 to 48, evaluate the given series. a (3  4k)5k=12a1...
 8.8.5.45: In Exercises 41 to 48, find the requested term. Find the middle ter...
 8.8.1.45: In Exercises 39 to 46, evaluate the factorial expression. 100!99!
 8.8.6.45: Ice Cream Cones An ice cream store offers 31 flavors of ice cream. ...
 8.8.2.45: Spider Webs The cross threads in a spider web are approximately equ...
 8.8.7.45: Preference Testing A software firm is considering marketing two new...
 8.8.3.45: In Exercises 37 to 46, find the sum of the finite geometric series....
 8.46: In Exercises 45 to 48, evaluate the given series. a25k=1 a (3  4k)
 8.8.5.46: In Exercises 41 to 48, find the requested term. Find the middle ter...
 8.8.1.46: In Exercises 39 to 46, evaluate the factorial expression. 100!98! 2!
 8.8.6.46: Computer Screens A typical computer monitor consists of pixels, eac...
 8.8.2.46: Spider Webs What is the sum of the lengths of the cross threads bet...
 8.8.7.46: Agriculture A fruit grower claims that onefourth of the orange tre...
 8.8.3.46: In Exercises 37 to 46, find the sum of the finite geometric series....
 8.47: In Exercises 45 to 48, evaluate the given series. aqn=1a 56bn1
 8.8.5.47: In Exercises 41 to 48, find the requested term. Find the two middle...
 8.8.1.47: In Exercises 47 to 60, evaluate the series. a5
 8.8.6.47: Dartboards How many different arrangements of the integers 1 throug...
 8.8.2.47: If f (x) is a linear polynomial, show that f (n), where n is a posi...
 8.8.7.47: Quality Control A quality control inspector receives a shipment of ...
 8.8.3.47: In Exercises 47 to 56, find the sum of the infinite geometric serie...
 8.48: In Exercises 45 to 48, evaluate the given series. aqn=12a34bn1
 8.8.5.48: In Exercises 41 to 48, find the requested term. Find the two middle...
 8.8.1.48: In Exercises 47 to 60, evaluate the series. 4i=1i2
 8.8.6.48: Lines in a Plane Generalize Exercise 37. That is, given n points in...
 8.8.2.48: Find the formula for an in terms of a1and n for the sequence that i...
 8.8.7.48: Lottery Consider a lottery that sells 1000 tickets and awards two p...
 8.8.3.48: In Exercises 47 to 56, find the sum of the infinite geometric serie...
 8.49: In Exercises 49 and 50, write each number as the ratio of two integ...
 8.8.5.49: In Exercises 49 to 54, use the Binomial Theorem to simplify the pow...
 8.8.1.49: In Exercises 47 to 60, evaluate the series. 5i=1i(i  1)
 8.8.6.49: Birthdays Seven people are asked the month of their birth. In how m...
 8.8.2.49: Find a formula for an in terms of a1 and n for the sequence that is...
 8.8.7.49: Airline Scheduling An airline estimates that 75% of the people who ...
 8.8.3.49: In Exercises 47 to 56, find the sum of the infinite geometric serie...
 8.50: In Exercises 49 and 50, write each number as the ratio of two integ...
 8.8.5.50: In Exercises 49 to 54, use the Binomial Theorem to simplify the pow...
 8.8.1.50: In Exercises 47 to 60, evaluate the series. 7i=1 a (2i + 1)
 8.8.6.50: Sums of Coins From a penny, a nickel, a dime, and a quarter, how ma...
 8.8.2.50: Suppose and are two sequences such that a1 = 4, an = bn1 + 5, and ...
 8.8.7.50: Airline Scheduling Suppose that an airplanes engines operate indepe...
 8.8.3.50: In Exercises 47 to 56, find the sum of the infinite geometric serie...
 8.51: In Exercises 51 to 58, determine whether the sequence is arithmetic...
 8.8.5.51: In Exercises 49 to 54, use the Binomial Theorem to simplify the pow...
 8.8.1.51: In Exercises 47 to 60, evaluate the series. 4k=11k
 8.8.6.51: Biology Five sticks of equal length are broken into a short piece a...
 8.8.2.51: Suppose and are two sequences such that a1 = 1, an = bn1 + 7, and ...
 8.8.7.51: Spread of a Rumor A club has nine members. One member starts a rumo...
 8.8.3.51: In Exercises 47 to 56, find the sum of the infinite geometric serie...
 8.52: In Exercises 51 to 58, determine whether the sequence is arithmetic...
 8.8.5.52: In Exercises 49 to 54, use the Binomial Theorem to simplify the pow...
 8.8.1.52: In Exercises 47 to 60, evaluate the series. a6k=11a k(k + 1)
 8.8.6.52: Arranging Numbers Four random digits are drawn (repetitions are all...
 8.8.7.52: Extrasensory Perception As a test for extrasensory perception (ESP)...
 8.8.3.52: In Exercises 47 to 56, find the sum of the infinite geometric serie...
 8.53: In Exercises 51 to 58, determine whether the sequence is arithmetic...
 8.8.5.53: In Exercises 49 to 54, use the Binomial Theorem to simplify the pow...
 8.8.1.53: In Exercises 47 to 60, evaluate the series. 8j=12j
 8.8.6.53: Random Walk An aimless tourist, standing on a street corner, tosses...
 8.8.7.53: Sports In some games, such as tennis, the winning player must win b...
 8.8.3.53: In Exercises 47 to 56, find the sum of the infinite geometric serie...
 8.54: In Exercises 51 to 58, determine whether the sequence is arithmetic...
 8.8.5.54: In Exercises 49 to 54, use the Binomial Theorem to simplify the pow...
 8.8.1.54: In Exercises 47 to 60, evaluate the series. a6i=1 a (2i + 1)(2i  1)
 8.8.7.54: Gambling One way that a player can win in a game of craps is to bet...
 8.8.3.54: In Exercises 47 to 56, find the sum of the infinite geometric serie...
 8.55: In Exercises 51 to 58, determine whether the sequence is arithmetic...
 8.8.1.55: In Exercises 47 to 60, evaluate the series. a i5i=1(1)i1 2
 8.8.3.55: In Exercises 47 to 56, find the sum of the infinite geometric serie...
 8.56: In Exercises 51 to 58, determine whether the sequence is arithmetic...
 8.8.1.56: In Exercises 47 to 60, evaluate the series. a4i=1(1)i12 a i
 8.8.3.56: In Exercises 47 to 56, find the sum of the infinite geometric serie...
 8.8.3.57: In Exercises 57 to 68, write each rational number as the ratio of t...
 8.57: In Exercises 51 to 58, determine whether the sequence is arithmetic...
 8.8.1.57: In Exercises 47 to 60, evaluate the series. a n + 17n=1log n + 1
 8.8.3.58: In Exercises 57 to 68, write each rational number as the ratio of t...
 8.58: In Exercises 51 to 58, determine whether the sequence is arithmetic...
 8.8.1.58: In Exercises 47 to 60, evaluate the series. a8n=2ln na n + 1
 8.8.3.59: In Exercises 57 to 68, write each rational number as the ratio of t...
 8.59: In Exercises 59 to 66, use mathematical induction to prove each sta...
 8.8.1.59: In Exercises 47 to 60, evaluate the series. a k!8k=08!k! (8  k)!
 8.8.3.60: In Exercises 57 to 68, write each rational number as the ratio of t...
 8.60: In Exercises 59 to 66, use mathematical induction to prove each sta...
 8.8.1.60: In Exercises 47 to 60, evaluate the series. a7k=01a k!
 8.8.3.61: In Exercises 57 to 68, write each rational number as the ratio of t...
 8.61: In Exercises 59 to 66, use mathematical induction to prove each sta...
 8.8.1.61: In Exercises 61 to 68, write the given series in summation notation...
 8.8.3.62: In Exercises 57 to 68, write each rational number as the ratio of t...
 8.62: In Exercises 59 to 66, use mathematical induction to prove each sta...
 8.8.1.62: In Exercises 61 to 68, write the given series in summation notation...
 8.8.3.63: In Exercises 57 to 68, write each rational number as the ratio of t...
 8.63: In Exercises 59 to 66, use mathematical induction to prove each sta...
 8.8.1.63: In Exercises 61 to 68, write the given series in summation notation...
 8.8.3.64: In Exercises 57 to 68, write each rational number as the ratio of t...
 8.64: In Exercises 59 to 66, use mathematical induction to prove each sta...
 8.8.1.64: In Exercises 61 to 68, write the given series in summation notation...
 8.8.3.65: In Exercises 57 to 68, write each rational number as the ratio of t...
 8.65: In Exercises 59 to 66, use mathematical induction to prove each sta...
 8.8.1.65: In Exercises 61 to 68, write the given series in summation notation...
 8.8.3.66: In Exercises 57 to 68, write each rational number as the ratio of t...
 8.66: In Exercises 59 to 66, use mathematical induction to prove each sta...
 8.8.1.66: In Exercises 61 to 68, write the given series in summation notation...
 8.8.3.67: In Exercises 57 to 68, write each rational number as the ratio of t...
 8.67: In Exercises 67 to 72, use the Binomial Theorem to expand each bino...
 8.8.1.67: In Exercises 61 to 68, write the given series in summation notation...
 8.8.3.68: In Exercises 57 to 68, write each rational number as the ratio of t...
 8.68: In Exercises 67 to 72, use the Binomial Theorem to expand each bino...
 8.8.1.68: In Exercises 61 to 68, write the given series in summation notation...
 8.8.3.69: Future Value of an Annuity Find the future value of an ordinary ann...
 8.69: In Exercises 67 to 72, use the Binomial Theorem to expand each bino...
 8.8.1.69: Newtons Method Newtons approximation to the square root of a number...
 8.8.3.70: Future Value of an Annuity To save for the replacement of a compute...
 8.70: In Exercises 67 to 72, use the Binomial Theorem to expand each bino...
 8.8.1.70: Imaginary Unit Let an = in, where i is the imaginary unit. Find the...
 8.8.3.71: Prosperity Club In 1935, the Prosperity Club chain letter was start...
 8.71: In Exercises 67 to 72, use the Binomial Theorem to expand each bino...
 8.8.1.71: Fibonacci Sequence For the Fibonacci sequence, add the first two te...
 8.8.3.72: Prosperity Club The population of the United States in 1935 was app...
 8.72: In Exercises 67 to 72, use the Binomial Theorem to expand each bino...
 8.8.1.72: Fibonacci Sequence Every natural number greater than 1 can be writt...
 8.8.3.73: Medicine The concentration (in milligrams per liter) of an antibiot...
 8.73: Car Options The buyer of a new car is offered 12 exterior colors an...
 8.8.1.73: Fibonacci Sequence The Binet form for the th term of the Fibonacci ...
 8.8.3.74: Medicine To treat some diseases, a patient must have a certain conc...
 8.74: Dinner Options A restaurant offers a prix fixe dinner that includes...
 8.8.3.75: Gordon Model of Stock Valuation Suppose Myna Alton purchases a stoc...
 8.75: Computer Passwords A computer password consists of eight letters. H...
 8.8.3.76: Gordon Model of Stock Valuation Use the Gordon model of stock valua...
 8.76: Serial Numbers The serial number on an airplane consists of the let...
 8.8.3.77: Gordon Model of Stock Valuation Suppose that a stock is paying a co...
 8.77: Committee Membership From a committee of 15 members, a president, a...
 8.8.3.78: Gordon Model of Stock Valuation Suppose that a stock is paying a co...
 8.78: Arranging Books Three of five different books are to be displayed o...
 8.8.3.79: Stock Valuation Explain why g must be less than i in the Gordon mod...
 8.79: Scheduling The emergency staff at a hospital consists of 4 supervis...
 8.8.3.80: Multiplier Effect Sometimes a city will argue that having a profess...
 8.80: Committee Membership From 12 people, a committee of 5 people is for...
 8.8.3.81: Multiplier Effect Suppose a city estimates that a new convention fa...
 8.81: Playing Cards How many different fourcard hands can be drawn witho...
 8.8.3.82: Counterfeit Money Circulation Suppose that $500,000 of counterfeit ...
 8.82: Playing Cards Two cards are drawn, without replacement, from the fo...
 8.8.3.83: Genealogy Some people can trace their ancestry back 10 generations,...
 8.83: Number Theory Three numbers are drawn from the digits 1 through 5, ...
 8.84: Tossing Coins A coin is tossed five times. List the elements in the...
 8.85: Dice Two dice are tossed. List the elements in the event that the s...
 8.86: Number Theory Two numbers are drawn, without replacement, from the ...
 8.87: Number Theory Let S = 5 Natural numbers less than or equal to 1006 ...
 8.88: Playing Cards A deck of 10 cards contains 5 red and 5 black cards. ...
 8.89: Playing Cards Which of the following has the greater probability: d...
 8.90: Sums of Coins A nickel, a dime, and a quarter are tossed. What is t...
 8.91: Medicine A company claims that its cold remedy is successful in red...
 8.92: Community Government A survey of members in a city council indicate...
 8.93: Employee Badges A room contains 12 employees who are wearing badges...
 8.94: Gordon Model of Stock Valuation Suppose a stock pays a dividend of ...
 8.95: Multiplier Effect Suppose a city estimates that a new sports facili...
Solutions for Chapter 8: Sequences, Series and Probability
Full solutions for College Algebra  7th Edition
ISBN: 9781439048610
Solutions for Chapter 8: Sequences, Series and Probability
Get Full SolutionsThis textbook survival guide was created for the textbook: College Algebra, edition: 7. Since 499 problems in chapter 8: Sequences, Series and Probability have been answered, more than 26573 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9781439048610. Chapter 8: Sequences, Series and Probability includes 499 full stepbystep solutions.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·