 13.13.2.1: In a(n) __ sequence, the difference between successive terms is a c...
 13.1: In 18, write down the first five terms of each sequence. (all) = {...
 13.13.1.1: For the function f(x) = x  I , find f(2) and f(3). (pp. 208219)
 13.13.4.1: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.1: If $1000 is invested at 4% per annum compounded semiannually, how m...
 13.13.5.1: The ____ is a triangular display of the binomial coefficients.
 13.13.2.2: True or False In an arithmetic sequence the sum of the first and la...
 13.2: In 18, write down the first five terms of each sequence. (bll) = {...
 13.13.1.2: True or False A function is a relation between two sets D and R so ...
 13.13.4.2: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.2: How much do you need to invest now at 5% per annum compounded month...
 13.13.5.2: () =___
 13.13.2.3: In 312, show that each sequence is arithmetic. Find the common dif...
 13.3: In 18, write down the first five terms of each sequence. (cll) = "...
 13.13.1.3: A(n) __ is a function whose domain is the set of positive integers.
 13.13.4.3: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.3: In a(n) ____ sequence the ratio of successive terms is a constant.
 13.13.5.3: True or False ( n ) = ( p) J n  J ! n!
 13.13.2.4: In 312, show that each sequence is arithmetic. Find the common dif...
 13.4: In 18, write down the first five terms of each sequence. (dn) = 
 13.13.1.4: For the sequence {sn} = {4n  I}, the first term is Sl = ___ and th...
 13.13.4.4: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.4: If 11'1 < 1, the sum of the geometric series 2: arkI k=1 is ___.
 13.13.5.4: The __ __ can be used to expand expressions like (2x + 3 )6.
 13.13.2.5: In 312, show that each sequence is arithmetic. Find the common dif...
 13.5: In 18, write down the first five terms of each sequence. (dn) = 
 13.13.1.5: L (2k) =___. k=l
 13.13.4.5: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.5: A sequence of equal periodic deposits is called a(n) ____.
 13.13.5.5: In 516, evaluate each expression. C)
 13.13.2.6: In 312, show that each sequence is arithmetic. Find the common dif...
 13.6: In 18, write down the first five terms of each sequence. al = 4;
 13.13.1.6: True or False Sequences are sometimes defined recursively.
 13.13.4.6: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.6: True or False A geometric sequence may be defined recursively.
 13.13.5.6: In 516, evaluate each expression. C)
 13.13.2.7: In 312, show that each sequence is arithmetic. Find the common dif...
 13.7: In 18, write down the first five terms of each sequence. al = 2; a...
 13.13.1.7: True or False A sequence is a function.
 13.13.4.7: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.7: True or False In a geometric sequence the common ratio is always a ...
 13.13.5.7: In 516, evaluate each expression. G)
 13.13.2.8: In 312, show that each sequence is arithmetic. Find the common dif...
 13.8: In 18, write down the first five terms of each sequence. al = 3; ...
 13.13.1.8: True or False L k = 3 k=1
 13.13.4.8: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.8: True or False For a geometric sequence with first term al and commo...
 13.13.5.8: In 516, evaluate each expression. ()
 13.13.2.9: In 312, show that each sequence is arithmetic. Find the common dif...
 13.9: In 9 and 10, write out each sum. 2,: (4k+2)k=i
 13.13.1.9: In 914, evaluate each factorial expression. 10!
 13.13.4.9: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.9: In 918, a geometric sequence is given. Find the common ratio and w...
 13.13.5.9: In 516, evaluate each expression. !)
 13.13.2.10: In 312, show that each sequence is arithmetic. Find the common dif...
 13.10: In 9 and 10, write out each sum. 32,: (3  k2)k=i
 13.13.1.10: In 914, evaluate each factorial expression. 9!
 13.13.4.10: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.10: In 918, a geometric sequence is given. Find the common ratio and w...
 13.13.5.10: In 516, evaluate each expression. (198)
 13.13.2.11: In 312, show that each sequence is arithmetic. Find the common dif...
 13.11: In 11 and 12, express each sum using summation notation. 1 +2 3...
 13.13.1.11: In 914, evaluate each factorial expression. 9! 6!
 13.13.4.11: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.11: In 918, a geometric sequence is given. Find the common ratio and w...
 13.13.5.11: In 516, evaluate each expression. ( 1000 ) 1000
 13.13.2.12: In 312, show that each sequence is arithmetic. Find the common dif...
 13.12: In 11 and 12, express each sum using summation notation. 2 +3+32 ...
 13.13.1.12: In 914, evaluate each factorial expression. 12! 1O!
 13.13.4.12: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.12: In 918, a geometric sequence is given. Find the common ratio and w...
 13.13.5.12: In 516, evaluate each expression. ( 1000 )
 13.13.2.13: In 1320, find the nth term of the arithmetic sequence (alII whose ...
 13.13: In 1324, determine whether the given sequence is arithmetic, geome...
 13.13.1.13: In 914, evaluate each factorial expression. 3! 7! 4!
 13.13.4.13: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.13: In 918, a geometric sequence is given. Find the common ratio and w...
 13.13.5.13: In 516, evaluate each expression. CD
 13.13.2.14: In 1320, find the nth term of the arithmetic sequence (alII whose ...
 13.14: In 1324, determine whether the given sequence is arithmetic, geome...
 13.13.1.14: In 914, evaluate each factorial expression. 5! 8! 3!
 13.13.4.14: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.14: In 918, a geometric sequence is given. Find the common ratio and w...
 13.13.5.14: In 516, evaluate each expression. G)
 13.13.2.15: In 1320, find the nth term of the arithmetic sequence (alII whose ...
 13.15: In 1324, determine whether the given sequence is arithmetic, geome...
 13.13.1.15: In 1526, write down the first five terms of each sequence. (snl = {n}
 13.13.4.15: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.15: In 918, a geometric sequence is given. Find the common ratio and w...
 13.13.5.15: In 516, evaluate each expression. G)
 13.13.2.16: In 1320, find the nth term of the arithmetic sequence (alII whose ...
 13.16: In 1324, determine whether the given sequence is arithmetic, geome...
 13.13.1.16: In 1526, write down the first five terms of each sequence. (sill =...
 13.13.4.16: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.16: In 918, a geometric sequence is given. Find the common ratio and w...
 13.13.5.16: In 516, evaluate each expression. ()
 13.13.2.17: In 1320, find the nth term of the arithmetic sequence (alII whose ...
 13.17: In 1324, determine whether the given sequence is arithmetic, geome...
 13.13.1.17: In 1526, write down the first five terms of each sequence. (alll =...
 13.13.4.17: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.17: In 918, a geometric sequence is given. Find the common ratio and w...
 13.13.5.17: In 1728, expand each expression using the Binomial Theorem. (x + 1)5
 13.13.2.18: In 1320, find the nth term of the arithmetic sequence (alII whose ...
 13.18: In 1324, determine whether the given sequence is arithmetic, geome...
 13.13.1.18: In 1526, write down the first five terms of each sequence. (bill =...
 13.13.4.18: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.18: In 918, a geometric sequence is given. Find the common ratio and w...
 13.13.5.18: In 1728, expand each expression using the Binomial Theorem. (x  1)5
 13.13.2.19: In 1320, find the nth term of the arithmetic sequence (alII whose ...
 13.19: In 1324, determine whether the given sequence is arithmetic, geome...
 13.13.1.19: In 1526, write down the first five terms of each sequence. (cnl = ...
 13.13.4.19: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.19: In 1932, determine whether the given sequence is arithmetic, geome...
 13.13.5.19: In 1728, expand each expression using the Binomial Theorem. (x  2)6
 13.13.2.20: In 1320, find the nth term of the arithmetic sequence (alII whose ...
 13.20: In 1324, determine whether the given sequence is arithmetic, geome...
 13.13.1.20: In 1526, write down the first five terms of each sequence. (dill =...
 13.13.4.20: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.20: In 1932, determine whether the given sequence is arithmetic, geome...
 13.13.5.20: In 1728, expand each expression using the Binomial Theorem. (x + 3)5
 13.13.2.21: In 2126, find the indicated term in each arithmetic sequence. 100t...
 13.21: In 1324, determine whether the given sequence is arithmetic, geome...
 13.13.1.21: In 1526, write down the first five terms of each sequence. (sill =...
 13.13.4.21: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.21: In 1932, determine whether the given sequence is arithmetic, geome...
 13.13.5.21: In 1728, expand each expression using the Binomial Theorem. (3x + 1)4
 13.13.2.22: In 2126, find the indicated term in each arithmetic sequence. 80th...
 13.22: In 1324, determine whether the given sequence is arithmetic, geome...
 13.13.1.22: In 1526, write down the first five terms of each sequence. sill = {I}
 13.13.4.22: In 122, use the Principle of Mathematical Induction to show that t...
 13.13.3.22: In 1932, determine whether the given sequence is arithmetic, geome...
 13.13.5.22: In 1728, expand each expression using the Binomial Theorem. (2x + 3)5
 13.13.5.23: In 1728, expand each expression using the Binomial Theorem. (x2 + l)5
 13.13.2.23: In 2126, find the indicated term in each arithmetic sequence. 90th...
 13.23: In 1324, determine whether the given sequence is arithmetic, geome...
 13.13.1.23: In 1526, write down the first five terms of each sequence. (till =...
 13.13.4.23: In 2327, prove each statement. If x > 1, then xn > 1.
 13.13.3.23: In 1932, determine whether the given sequence is arithmetic, geome...
 13.13.5.24: In 1728, expand each expression using the Binomial Theorem. (x2  l)6
 13.13.2.24: In 2126, find the indicated term in each arithmetic sequence. 80th...
 13.24: In 1324, determine whether the given sequence is arithmetic, geome...
 13.13.1.24: In 1526, write down the first five terms of each sequence. (alll =...
 13.13.4.24: In 2327, prove each statement. If 0 < x < 1, then 0 < xn < 1.
 13.13.3.24: In 1932, determine whether the given sequence is arithmetic, geome...
 13.13.5.25: In 1728, expand each expression using the Binomial Theorem. (\IX +...
 13.13.2.25: In 2126, find the indicated term in each arithmetic sequence. 80th...
 13.25: In 2530, find each sum. 50 (3k)k=l
 13.13.1.25: In 1526, write down the first five terms of each sequence. (bill =...
 13.13.4.25: In 2327, prove each statement. a  b is a factor of an  bn.[Hint:...
 13.13.3.25: In 1932, determine whether the given sequence is arithmetic, geome...
 13.13.5.26: In 1728, expand each expression using the Binomial Theorem. (\IX ...
 13.13.2.26: In 2126, find the indicated term in each arithmetic sequence. 70th...
 13.26: In 2530, find each sum. 30 k2k=l
 13.13.1.26: In 1526, write down the first five terms of each sequence. (clll =...
 13.13.4.26: In 2327, prove each statement. a + b is a factor of a2n+ 1 + b2//+I.
 13.13.3.26: In 1932, determine whether the given sequence is arithmetic, geome...
 13.13.5.27: In 1728, expand each expression using the Binomial Theorem. (ax + ...
 13.13.2.27: In 2734, find the first term and the common difference of the arit...
 13.27: In 2530, find each sum. 30 (3k  9)k=l
 13.13.1.27: In 2734, the given pattern continues. Write down the nth term of a...
 13.13.4.27: In 2327, prove each statement. (1 + a)" 1 + na, for a > 0
 13.13.3.27: In 1932, determine whether the given sequence is arithmetic, geome...
 13.13.5.28: In 1728, expand each expression using the Binomial Theorem. (ax  ...
 13.13.2.28: In 2734, find the first term and the common difference of the arit...
 13.28: In 2530, find each sum.40 ( 2k + 8)k=l
 13.13.1.28: In 2734, the given pattern continues. Write down the nth term of a...
 13.13.4.28: Show that the statement " n2  n + 41 is a prime number" is true fo...
 13.13.3.28: In 1932, determine whether the given sequence is arithmetic, geome...
 13.13.5.29: In 2942, use the Binomial Theorem to find the indicated coefficien...
 13.13.2.29: In 2734, find the first term and the common difference of the arit...
 13.29: In 2530, find each sum. 7 (l)k ::;k=\ 
 13.13.1.29: In 2734, the given pattern continues. Write down the nth term of a...
 13.13.4.29: Show that the formula 2 + 4 + 6 + . . . + 2n = n2 + n + 2 obeys Con...
 13.13.3.29: In 1932, determine whether the given sequence is arithmetic, geome...
 13.13.5.30: In 2942, use the Binomial Theorem to find the indicated coefficien...
 13.13.2.30: In 2734, find the first term and the common difference of the arit...
 13.30: In 2530, find each sum. 10 (_2)kk=l
 13.13.1.30: In 2734, the given pattern continues. Write down the nth term of a...
 13.13.4.30: Use mathematical induction to prove that if r =f. 1 then 1  r// a ...
 13.13.3.30: In 1932, determine whether the given sequence is arithmetic, geome...
 13.13.5.31: In 2942, use the Binomial Theorem to find the indicated coefficien...
 13.13.2.31: In 2734, find the first term and the common difference of the arit...
 13.31: In 3136, find the indicated term in each sequence. [Hint: Find the...
 13.13.1.31: In 2734, the given pattern continues. Write down the nth term of a...
 13.13.4.31: Use mathematical induction to prove that a + (a + d) + (a + 2d) I ...
 13.13.3.31: In 1932, determine whether the given sequence is arithmetic, geome...
 13.13.5.32: In 2942, use the Binomial Theorem to find the indicated coefficien...
 13.13.2.32: In 2734, find the first term and the common difference of the arit...
 13.32: In 3136, find the indicated term in each sequence. [Hint: Find the...
 13.13.1.32: In 2734, the given pattern continues. Write down the nth term of a...
 13.13.4.32: Extended Principle of Mathematical Induction The Extended Principle...
 13.13.3.32: In 1932, determine whether the given sequence is arithmetic, geome...
 13.13.5.33: In 2942, use the Binomial Theorem to find the indicated coefficien...
 13.13.2.33: In 2734, find the first term and the common difference of the arit...
 13.33: In 3136, find the indicated term in each sequence. [Hint: Find the...
 13.13.1.33: In 2734, the given pattern continues. Write down the nth term of a...
 13.13.4.33: Geometry Use the Extended Principle of Mathematical Induction to sh...
 13.13.3.33: In 3340, find the fifth term and the nth term of the geometric seq...
 13.13.5.34: In 2942, use the Binomial Theorem to find the indicated coefficien...
 13.13.2.34: In 2734, find the first term and the common difference of the arit...
 13.34: In 3136, find the indicated term in each sequence. [Hint: Find the...
 13.13.1.34: In 2734, the given pattern continues. Write down the nth term of a...
 13.13.3.34: In 3340, find the fifth term and the nth term of the geometric seq...
 13.13.5.35: In 2942, use the Binomial Theorem to find the indicated coefficien...
 13.13.2.35: In 3552, find each sum. 1 + 3 + 5 + . . . + (2n  1)
 13.35: In 3136, find the indicated term in each sequence. [Hint: Find the...
 13.13.1.35: In 3548, a sequence is defined recursively. Write down the first f...
 13.13.3.35: In 3340, find the fifth term and the nth term of the geometric seq...
 13.13.5.36: In 2942, use the Binomial Theorem to find the indicated coefficien...
 13.13.2.36: In 3552, find each sum. 2 + 4 + 6 + ... + 2n
 13.36: In 3136, find the indicated term in each sequence. [Hint: Find the...
 13.13.1.36: In 3548, a sequence is defined recursively. Write down the first f...
 13.13.3.36: In 3340, find the fifth term and the nth term of the geometric seq...
 13.13.5.37: In 2942, use the Binomial Theorem to find the indicated coefficien...
 13.13.2.37: In 3552, find each sum. 7 + 12 + 17 + ... + (2 + 5n)
 13.37: In 3740, find a general formula for each arithmetic sequence. 7th ...
 13.13.1.37: In 3548, a sequence is defined recursively. Write down the first f...
 13.13.3.37: In 3340, find the fifth term and the nth term of the geometric seq...
 13.13.5.38: In 2942, use the Binomial Theorem to find the indicated coefficien...
 13.13.2.38: In 3552, find each sum. 1 + 3 + 7 + . . . + (4n  5)
 13.38: In 3740, find a general formula for each arithmetic sequence. 8th ...
 13.13.1.38: In 3548, a sequence is defined recursively. Write down the first f...
 13.13.3.38: In 3340, find the fifth term and the nth term of the geometric seq...
 13.13.5.39: In 2942, use the Binomial Theorem to find the indicated coefficien...
 13.13.2.39: In 3552, find each sum. 2 + 4 + 6 + ... + 70
 13.39: In 3740, find a general formula for each arithmetic sequence. 10th...
 13.13.1.39: In 3548, a sequence is defined recursively. Write down the first f...
 13.13.3.39: In 3340, find the fifth term and the nth term of the geometric seq...
 13.13.5.40: In 2942, use the Binomial Theorem to find the indicated coefficien...
 13.13.2.40: In 3552, find each sum. 1 + 3 + 5 + . . . + 59
 13.40: In 3740, find a general formula for each arithmetic sequence. 12th...
 13.13.1.40: In 3548, a sequence is defined recursively. Write down the first f...
 13.13.3.40: In 3340, find the fifth term and the nth term of the geometric seq...
 13.13.3.41: In 4146, find the indicated term of each geometric sequence. 7th t...
 13.13.5.41: In 2942, use the Binomial Theorem to find the indicated coefficien...
 13.13.2.41: In 3552, find each sum. 5 + 9 + 13 + ... + 49
 13.41: In 4148, determine whether each infinite geometric series converge...
 13.13.1.41: In 3548, a sequence is defined recursively. Write down the first f...
 13.13.3.42: In 4146, find the indicated term of each geometric sequence. 8th t...
 13.13.5.42: In 2942, use the Binomial Theorem to find the indicated coefficien...
 13.13.2.42: In 3552, find each sum. 2 + 5 + 8 + ... + 41
 13.42: In 4148, determine whether each infinite geometric series converge...
 13.13.1.42: In 3548, a sequence is defined recursively. Write down the first f...
 13.13.3.43: In 4146, find the indicated term of each geometric sequence. 9th t...
 13.13.5.43: Use the Binomial Theorem to find the numerical value of (1.001)5 co...
 13.13.2.43: In 3552, find each sum. 73 + 78 + 83 + 88 + ... + 558
 13.43: In 4148, determine whether each infinite geometric series converge...
 13.13.1.43: In 3548, a sequence is defined recursively. Write down the first f...
 13.13.3.44: In 4146, find the indicated term of each geometric sequence. 10th ...
 13.13.5.44: Use the Binomial Theorem to find the numerical value of (0.998)6 co...
 13.13.2.44: In 3552, find each sum. 7+ 1  5  1 1  299
 13.44: In 4148, determine whether each infinite geometric series converge...
 13.13.1.44: In 3548, a sequence is defined recursively. Write down the first f...
 13.13.3.45: In 4146, find the indicated term of each geometric sequence. 8th t...
 13.13.5.45: Show that C : 1 ) = n and (: ) = 1.
 13.13.2.45: In 3552, find each sum. 4 + 4.5 + 5 + 5.5 + ... + 100
 13.45: In 4148, determine whether each infinite geometric series converge...
 13.13.1.45: In 3548, a sequence is defined recursively. Write down the first f...
 13.13.3.46: In 4146, find the indicated term of each geometric sequence. 7th t...
 13.13.5.46: Show that if n and j are integers with a j n then Conclude that the...
 13.13.2.46: In 3552, find each sum. 8 + 8 + 8 + 8 + 9 + ... + 50 424
 13.46: In 4148, determine whether each infinite geometric series converge...
 13.13.1.46: In 3548, a sequence is defined recursively. Write down the first f...
 13.13.3.47: In 4754, find the nth term all of each geometric sequence. When gi...
 13.13.5.47: If n is a positive integer, show that [Hint: 21/ = (1 + 1)"; now us...
 13.13.2.47: In 3552, find each sum. 802:(2n  5)
 13.47: In 4148, determine whether each infinite geometric series converge...
 13.13.1.47: In 3548, a sequence is defined recursively. Write down the first f...
 13.13.3.48: In 4754, find the nth term all of each geometric sequence. When gi...
 13.13.5.48: If n is a positive integer, show that (z)  () + G) . .. + (1)''(...
 13.13.2.48: In 3552, find each sum. 90 2: (3  2n)11 =1
 13.48: In 4148, determine whether each infinite geometric series converge...
 13.13.1.48: In 3548, a sequence is defined recursively. Write down the first f...
 13.13.3.49: In 4754, find the nth term all of each geometric sequence. When gi...
 13.13.5.49: ()GY + G)()4G) + G)(YGY + C)GYGY + C)G)GY + G)(Y = ?
 13.13.2.49: In 3552, find each sum. JOO ( 1 ) 2: 6   n11=1 2
 13.49: In 4954, use the Principle of Mathematical Induction to show that ...
 13.13.1.49: In 4958, write out each sum. 11 nL (k + 2) k=l11
 13.13.3.50: In 4754, find the nth term all of each geometric sequence. When gi...
 13.13.5.50: Stirling's Formula An approximation for n!, when n is large, is giv...
 13.13.2.50: In 3552, find each sum. 80 ( 1 1 ) 2: n + 11 =1 3 2
 13.50: In 4954, use the Principle of Mathematical Induction to show that ...
 13.13.1.50: In 4958, write out each sum. L (2k + 1)
 13.13.3.51: In 4754, find the nth term all of each geometric sequence. When gi...
 13.13.2.51: In 3552, find each sum. The sum of the first 120 terms of the sequ...
 13.51: In 4954, use the Principle of Mathematical Induction to show that ...
 13.13.1.51: In 4958, write out each sum. L k2 k = 11
 13.13.3.52: In 4754, find the nth term all of each geometric sequence. When gi...
 13.13.2.52: In 3552, find each sum. The sum of the first 46 terms of the seque...
 13.52: In 4954, use the Principle of Mathematical Induction to show that ...
 13.13.1.52: In 4958, write out each sum. n 1 L (k + 1)2
 13.13.3.53: In 4754, find the nth term all of each geometric sequence. When gi...
 13.13.2.53: Find x so that x + 3, 2x + 1, and 5x + 2 are consecutive terms of a...
 13.53: In 4954, use the Principle of Mathematical Induction to show that ...
 13.13.1.53: In 4958, write out each sum. n 1k = 03k
 13.13.3.54: In 4754, find the nth term all of each geometric sequence. When gi...
 13.13.2.54: Find x so that 2x, 3x + 2, and 5x + 3 are consecutive terms of an a...
 13.54: In 4954, use the Principle of Mathematical Induction to show that ...
 13.13.1.54: In 4958, write out each sum. 11 CY n1 1L  k=O
 13.13.3.55: In 5560, find each sum. 1 2 22 23 2111  + + +  + .. 4 4 4 4.....
 13.13.2.55: Drury Lane Theater The Drury Lane Theater has 25 seats in the first...
 13.55: In 55 and 56, evaluate each binomial coefficient. G)
 13.13.1.55: In 4958, write out each sum. n1 1L k+lk=o 3
 13.13.3.56: In 5560, find each sum. 3 32 33 311 +  +  + ... + 9 9 9 9
 13.13.2.56: Football Stadium The corner section of a football stadium has 15 se...
 13.56: In 55 and 56, evaluate each binomial coefficient. G)
 13.13.1.56: In 4958, write out each sum. 111 L (2k + 1) k=O
 13.13.3.57: In 5560, find each sum. i ()kk=1 3
 13.13.2.57: Creating a Mosaic A mosaic is designed in the shape of an equilater...
 13.57: In 5760, expand each expression using the Binomial Theorem. (x + 2)5
 13.13.1.57: In 4958, write out each sum. 11 nkln k k=2
 13.13.3.58: In 5560, find each sum. 2.: 4 3k1k=l
 13.13.2.58: Constructing a Brick Staircase A brick staircase has a total of 30 ...
 13.58: In 5760, expand each expression using the Binomial Theorem. (x  3)4
 13.13.1.58: In 4958, write out each sum. L (_1)k+12kk=3
 13.13.3.59: In 5560, find each sum. 1 2 4 8  ...  (2"1)
 13.13.2.59: Cooling Air As a parcel of air rises (for example, as it is pushed ...
 13.59: In 5760, expand each expression using the Binomial Theorem. (2x + 3)5
 13.13.1.59: In 5968, express each sum using summation notation. 1 + 2 + 3 + . ...
 13.13.3.60: In 5560, find each sum. 2 +  +  + ... + 2 5 25 5
 13.13.2.60: Citrus Ladders Ladders used by fruit pickers are typically tapered ...
 13.60: In 5760, expand each expression using the Binomial Theorem. (3x 4)4
 13.13.1.60: In 5968, express each sum using summation notation. 13 + 23 + 33 +...
 13.13.3.61: For 6166, use a graphing utility to find the sum of each geometric...
 13.13.2.61: Seats in an Aml )hitheater An outdoor amphitheater has 35 seats in ...
 13.61: Find the coefficient of x7 in the expansion of (x + 2t
 13.13.1.61: In 5968, express each sum using summation notation. 1 2 3 13 2 + 3...
 13.13.3.62: For 6166, use a graphing utility to find the sum of each geometric...
 13.13.2.62: Stadium Construction How many rows are in the corner section of a s...
 13.62: Find the coefficient of x3 in the expansion of (x  3)8.
 13.13.1.62: In 5968, express each sum using summation notation. 1 + 3 + 5 + 7 ...
 13.13.3.63: For 6166, use a graphing utility to find the sum of each geometric...
 13.13.2.63: Salary Suppose that you j ust received a job offer with a starting ...
 13.63: Find the coefficient of x 2 in the expansion of (2x + 1)7.
 13.13.1.63: In 5968, express each sum using summation notation.   +  + . ...
 13.13.3.64: For 6166, use a graphing utility to find the sum of each geometric...
 13.13.2.64: Make up an arithmetic sequence. Give it to a friend and ask for its...
 13.64: Find the coefficient of x 6 in the expansion of (2x + 1 )8.
 13.13.1.64: In 5968, express each sum using summation notation. 2 4 8 (2)113 ...
 13.13.3.65: For 6166, use a graphing utility to find the sum of each geometric...
 13.13.2.65: Describe the similarities and differences between arithmetic sequen...
 13.65: Constructing a Brick Staircase A brick staircase has a total of 25 ...
 13.13.1.65: In 5968, express each sum using summation notation. 3 +  +  + .....
 13.13.3.66: For 6166, use a graphing utility to find the sum of each geometric...
 13.66: Creating a Floor Design A mosaic tile floor is designed in the shap...
 13.13.1.66: In 5968, express each sum using summation notation. 1 2 3 n  +  ...
 13.13.3.67: In 6782, determine whether each infinite geometric series converge...
 13.67: Bouncing Balls A ball is dropped from a height of 20 feet. Each tim...
 13.13.1.67: In 5968, express each sum using summation notation. a + (a + d) + ...
 13.13.3.68: In 6782, determine whether each infinite geometric series converge...
 13.68: Retirement Planning Chris gets paid once a month and contributes $2...
 13.13.1.68: In 5968, express each sum using summation notation. a + ar + ar2 +...
 13.13.3.69: In 6782, determine whether each infinite geometric series converge...
 13.69: Retirement Planning Jacky contributes $500 every quarter to an IRA....
 13.13.1.69: In 6980, find the sum of each sequence. 2: 5 k=l
 13.13.3.70: In 6782, determine whether each infinite geometric series converge...
 13.70: Salary Increases Your friend has just been hired at an annual salar...
 13.13.1.70: In 6980, find the sum of each sequence. 508k=l
 13.13.3.71: In 6782, determine whether each infinite geometric series converge...
 13.13.1.71: In 6980, find the sum of each sequence. 402:kk = l
 13.13.3.72: In 6782, determine whether each infinite geometric series converge...
 13.13.1.72: In 6980, find the sum of each sequence. 242: (k)k= l
 13.13.1.73: In 6980, find the sum of each sequence. 20262: (3k  7)k=l
 13.13.3.73: In 6782, determine whether each infinite geometric series converge...
 13.13.1.74: In 6980, find the sum of each sequence. 262: (3k  7)k=1
 13.13.3.74: In 6782, determine whether each infinite geometric series converge...
 13.13.1.75: In 6980, find the sum of each sequence. 2: (k2 + 4)k=1
 13.13.3.75: In 6782, determine whether each infinite geometric series converge...
 13.13.1.76: In 6980, find the sum of each sequence. 142: (k2  4)k=O
 13.13.3.76: In 6782, determine whether each infinite geometric series converge...
 13.13.1.77: In 6980, find the sum of each sequence. 2: (2k) k=lO
 13.13.3.77: In 6782, determine whether each infinite geometric series converge...
 13.13.1.78: In 6980, find the sum of each sequence. 402: (3k)k=8
 13.13.3.78: In 6782, determine whether each infinite geometric series converge...
 13.13.1.79: In 6980, find the sum of each sequence. 202: k3k=5
 13.13.3.79: In 6782, determine whether each infinite geometric series converge...
 13.13.1.80: In 6980, find the sum of each sequence. 242: k3k=4
 13.13.3.80: In 6782, determine whether each infinite geometric series converge...
 13.13.1.81: Credit Card Debt John has a balance of $3000 on his Discover card t...
 13.13.3.81: In 6782, determine whether each infinite geometric series converge...
 13.13.1.82: Trout Population A pond currently has 2000 trout in it. A fish hatc...
 13.13.3.82: In 6782, determine whether each infinite geometric series converge...
 13.13.1.83: Car Loans Phil bought a car by taking out a loan for $18,500 at 0.5...
 13.13.3.83: Find x so that x, x + 2, and x + 3 are consecutive terms of a geome...
 13.13.1.84: Environmental Control The Environmental Protection Agency (EPA) det...
 13.13.3.84: Find x so that x  1, x, and x + 2 are consecutive terms of a geome...
 13.13.1.85: Growth of a Rabbit Colony A colony of rabbits begins with one pair ...
 13.13.3.85: Salary Increases Suppose that you have j ust been hired at an annua...
 13.13.1.86: Fibonacci Sequence Let Un = (1 + vs)"  (1  vs)n 2 nVS define the ...
 13.13.3.86: Equipment Depreciation A new piece of equipment cost a company $15,...
 13.13.1.87: Pascal's Triangle Divide the triangular array shown (called Pascal'...
 13.13.3.87: Pendulum Swings Initially, a pendulum swings through an arc of 2 fe...
 13.13.1.88: Fibonacci Sequence Use the result of to do the following problems: ...
 13.13.3.88: Bouncing Balls A ball is dropped from a height of 30 feet. Each tim...
 13.13.1.89: Approximating I(x) = e ' In calculus, it can be shown that 00 x k [...
 13.13.3.89: Retirement Christine contributes $100 each month to her 401(k). Wha...
 13.13.1.90: Approximating I(x) = e ' Refer to 89. (a) Approximate [(  2.4) wit...
 13.13.3.90: SaYing for a Home Jolene wants to purchase a new home. Suppose that...
 13.13.1.91: Bode's Law In 1772, Johann Bode published the following formula for...
 13.13.3.91: Tax Sheltered Annuity Don contributes $500 at the end of each quart...
 13.13.1.92: Show that n(n + 1) 1 + 2 + ... + (n  1) + n = 2 [Hint: Let s =...
 13.13.3.92: Retirement Ray contributes $1 000 to an Individual Retirement Accou...
 13.13.1.93: Investigate various applications that lead to a Fibonacci sequence,...
 13.13.3.93: Sinking Fund Scott and Alice want to purchase a vacation home in 10...
 13.13.3.94: Sinking Fund For a child born in 1 996, a 4year college education ...
 13.13.3.95: Grains of Wheat on a Chess Board In an old fable, a commoner who ha...
 13.13.3.96: Look at the figure. What fraction of the square is eventually shade...
 13.13.3.97: Multiplier Suppose that, throughout the U.S. economy, individuals s...
 13.13.3.98: Multiplier Refer to 97. Suppose that the marginal propensity to con...
 13.13.3.99: Stock Price One method of pricing a stock is to discount the stream...
 13.13.3.100: Stock Price Refer to 99. Suppose that a stock pays an annual divide...
 13.13.3.101: A Rich Man's Promise A rich man promises to give you $1000 on Septe...
 13.13.3.102: Critical Thinking You are interviewing for a job and receive two of...
 13.13.3.103: Critical Thinking Which of the following choices, A or B, results i...
 13.13.3.104: Critical Thinking You have just signed a 7year professional footba...
 13.13.3.105: Critical Thinking Suppose you were offered a job in which you would...
 13.13.3.106: Can a sequence be both arithmetic and geometric? Give reasons for y...
 13.13.3.107: Make up a geometric sequence. Give it to a friend and ask for its 2...
 13.13.3.108: Make up two infinite geometric series, one that has a sum and one t...
 13.13.3.109: Describe the similarities and differences between geometric sequenc...
Solutions for Chapter 13: Sequences, Induction; and Binomial Theorem
Full solutions for Algebra and Trigonometry  8th Edition
ISBN: 9780132329033
Solutions for Chapter 13: Sequences, Induction; and Binomial Theorem
Get Full SolutionsSince 420 problems in chapter 13: Sequences, Induction; and Binomial Theorem have been answered, more than 87320 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9780132329033. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8. Chapter 13: Sequences, Induction; and Binomial Theorem includes 420 full stepbystep solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

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

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

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 ().

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.