 8.1.1: Fill in each blank so that the resulting statement is true. {an} = ...
 8.1.2: Fill in each blank so that the resulting statement is true. The nth...
 8.1.3: Fill in each blank so that the resulting statement is true. Write t...
 8.1.4: Fill in each blank so that the resulting statement is true. Write t...
 8.1.5: Fill in each blank so that the resulting statement is true. Write t...
 8.1.6: Fill in each blank so that the resulting statement is true. 5!, cal...
 8.1.7: Fill in each blank so that the resulting statement is true. (n + 3)...
 8.1.8: Fill in each blank so that the resulting statement is true. ani=1ai...
 8.1.9: In Exercises 112, write the first four terms of each sequence whose...
 8.1.10: In Exercises 112, write the first four terms of each sequence whose...
 8.1.11: In Exercises 112, write the first four terms of each sequence whose...
 8.1.12: In Exercises 112, write the first four terms of each sequence whose...
 8.1.13: The sequences in Exercises 1318 are defined using recursion formula...
 8.1.14: The sequences in Exercises 1318 are defined using recursion formula...
 8.1.15: The sequences in Exercises 1318 are defined using recursion formula...
 8.1.16: The sequences in Exercises 1318 are defined using recursion formula...
 8.1.17: The sequences in Exercises 1318 are defined using recursion formula...
 8.1.18: The sequences in Exercises 1318 are defined using recursion formula...
 8.1.19: In Exercises 1922, the general term of a sequence is given and invo...
 8.1.20: In Exercises 1922, the general term of a sequence is given and invo...
 8.1.21: In Exercises 1922, the general term of a sequence is given and invo...
 8.1.22: In Exercises 1922, the general term of a sequence is given and invo...
 8.1.23: In Exercises 2328, evaluate each factorial expression. 17!15!
 8.1.24: In Exercises 2328, evaluate each factorial expression. 18!16!
 8.1.25: In Exercises 2328, evaluate each factorial expression. 16!2!14!
 8.1.26: In Exercises 2328, evaluate each factorial expression. 20!2!18!
 8.1.27: In Exercises 2328, evaluate each factorial expression. (n + 2)!n!
 8.1.28: In Exercises 2328, evaluate each factorial expression. (2n + 1)!(2n)!
 8.1.29: In Exercises 2942, find each indicated sum. 6i=15i
 8.1.30: In Exercises 2942, find each indicated sum. 6i=17i
 8.1.31: In Exercises 2942, find each indicated sum. 4i=12i2
 8.1.32: In Exercises 2942, find each indicated sum. 5i=1i3
 8.1.33: In Exercises 2942, find each indicated sum. a5k=1k(k + 4)
 8.1.34: In Exercises 2942, find each indicated sum. a4k=1(k  3)(k + 2)
 8.1.35: In Exercises 2942, find each indicated sum. 4i=1a  12bi
 8.1.36: In Exercises 2942, find each indicated sum. a4i=2a  13bi
 8.1.37: In Exercises 2942, find each indicated sum. a9i=511
 8.1.38: In Exercises 2942, find each indicated sum. a7i=312
 8.1.39: In Exercises 2942, find each indicated sum. a4i=0(1)ii!
 8.1.40: In Exercises 2942, find each indicated sum. a4i=0(1)i+1(i + 1)!
 8.1.41: In Exercises 2942, find each indicated sum. a5i=1i!(i  1)!
 8.1.42: In Exercises 2942, find each indicated sum. a5i=1(i + 2)!i!
 8.1.43: In Exercises 4354, express each sum using summation notation. Use 1...
 8.1.44: In Exercises 4354, express each sum using summation notation. Use 1...
 8.1.45: In Exercises 4354, express each sum using summation notation. Use 1...
 8.1.46: In Exercises 4354, express each sum using summation notation. Use 1...
 8.1.47: In Exercises 4354, express each sum using summation notation. Use 1...
 8.1.48: In Exercises 4354, express each sum using summation notation. Use 1...
 8.1.49: In Exercises 4354, express each sum using summation notation. Use 1...
 8.1.50: In Exercises 4354, express each sum using summation notation. Use 1...
 8.1.51: In Exercises 4354, express each sum using summation notation. Use 1...
 8.1.52: In Exercises 4354, express each sum using summation notation. Use 1...
 8.1.53: In Exercises 4354, express each sum using summation notation. Use 1...
 8.1.54: In Exercises 4354, express each sum using summation notation. Use 1...
 8.1.55: In Exercises 5560, express each sum using summation notation. Use a...
 8.1.56: In Exercises 5560, express each sum using summation notation. Use a...
 8.1.57: In Exercises 5560, express each sum using summation notation. Use a...
 8.1.58: In Exercises 5560, express each sum using summation notation. Use a...
 8.1.59: In Exercises 5560, express each sum using summation notation. Use a...
 8.1.60: In Exercises 5560, express each sum using summation notation. Use a...
 8.1.61: In Exercises 6168, use the graphs of {an} and {bn} to find each ind...
 8.1.62: In Exercises 6168, use the graphs of {an} and {bn} to find each ind...
 8.1.63: In Exercises 6168, use the graphs of {an} and {bn} to find each ind...
 8.1.64: In Exercises 6168, use the graphs of {an} and {bn} to find each ind...
 8.1.65: In Exercises 6168, use the graphs of {an} and {bn} to find each ind...
 8.1.66: In Exercises 6168, use the graphs of {an} and {bn} to find each ind...
 8.1.67: In Exercises 6168, use the graphs of {an} and {bn} to find each ind...
 8.1.68: In Exercises 6168, use the graphs of {an} and {bn} to find each ind...
 8.1.69: The bar graph at the top of the next column shows the average numbe...
 8.1.70: The bar graph shows the number of Americans who renounced their U.S...
 8.1.71: A deposit of $6000 is made in an account that earns 6% interest com...
 8.1.72: A deposit of $10,000 is made in an account that earns 8% interest c...
 8.1.73: What is a sequence? Give an example with your description.
 8.1.74: Explain how to write terms of a sequence if the formula for the gen...
 8.1.75: What does the graph of a sequence look like? How is it obtained?
 8.1.76: What is a recursion formula?
 8.1.77: Explain how to find n! if n is a positive integer.
 8.1.78: Explain the best way to evaluate 900! 899! without a calculator.
 8.1.79: What is the meaning of the symbol g? Give an example with your desc...
 8.1.80: You buy a new car for $24,000. At the end of n years, the value of ...
 8.1.81: In Exercises 8185, use a calculators factorial key to evaluate each...
 8.1.82: In Exercises 8185, use a calculators factorial key to evaluate each...
 8.1.83: In Exercises 8185, use a calculators factorial key to evaluate each...
 8.1.84: In Exercises 8185, use a calculators factorial key to evaluate each...
 8.1.85: In Exercises 8185, use a calculators factorial key to evaluate each...
 8.1.86: Use the SEQ(sequence) capability of a graphing utility to verify th...
 8.1.87: Use the SUMSEQ (sum of the sequence) capability of a graphing utili...
 8.1.88: As n increases, the terms of the sequence an = a1 + 1 n b n get clo...
 8.1.89: Many graphing utilities have a sequencegraphing mode that plots th...
 8.1.90: Many graphing utilities have a sequencegraphing mode that plots th...
 8.1.91: Many graphing utilities have a sequencegraphing mode that plots th...
 8.1.92: Many graphing utilities have a sequencegraphing mode that plots th...
 8.1.93: In Exercises 9396, determine whether each statement makes sense or ...
 8.1.94: In Exercises 9396, determine whether each statement makes sense or ...
 8.1.95: In Exercises 9396, determine whether each statement makes sense or ...
 8.1.96: In Exercises 9396, determine whether each statement makes sense or ...
 8.1.97: In Exercises 97100, determine whether each statement is true or fal...
 8.1.98: In Exercises 97100, determine whether each statement is true or fal...
 8.1.99: In Exercises 97100, determine whether each statement is true or fal...
 8.1.100: In Exercises 97100, determine whether each statement is true or fal...
 8.1.101: Write the first five terms of the sequence whose first term is 9 an...
 8.1.102: Enough curiosities involving the Fibonacci sequence exist to warran...
 8.1.103: Solve: x x  3 = 2x x  3  5 3 . (Section 1.2, Example 5)
 8.1.104: Use the graph of y = f(x) to graph y = f(x  2)  1. 1 1 2 3 4 2 3 ...
 8.1.105: Solve: x4  6x3 + 4x2 + 15x + 4 = 0. (Section 3.4, Example 5)
 8.1.106: Exercises 106108 will help you prepare for the material covered in ...
 8.1.107: Exercises 106108 will help you prepare for the material covered in ...
 8.1.108: Exercises 106108 will help you prepare for the material covered in ...
Solutions for Chapter 8.1: Sequences and Summation Notation
Full solutions for College Algebra  7th Edition
ISBN: 9780134469164
Solutions for Chapter 8.1: Sequences and Summation Notation
Get Full SolutionsThis textbook survival guide was created for the textbook: College Algebra , edition: 7. Since 108 problems in chapter 8.1: Sequences and Summation Notation have been answered, more than 30845 students have viewed full stepbystep solutions from this chapter. College Algebra was written by and is associated to the ISBN: 9780134469164. Chapter 8.1: Sequences and Summation Notation includes 108 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

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

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

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

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

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

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

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 .

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

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

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

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.