 11.1.1: An ________ ________ is a function whose domain is the set of posit...
 11.1.2: The function values are called the ________ of a sequence.
 11.1.3: A sequence is a ________ sequence if the domain of the function con...
 11.1.4: If you are given one or more of the first few terms of a sequence, ...
 11.1.5: If is a positive integer, ________ is defined as
 11.1.6: The notation used to represent the sum of the terms of a finite seq...
 11.1.7: For the sum is called the ________ of summation, is the ________ li...
 11.1.8: The sum of the terms of a finite or infinite sequence is called a _...
 11.1.9:
 11.1.10:
 11.1.11: an
 11.1.12: an 1 2
 11.1.13: an 2n
 11.1.14: an 1 2
 11.1.15: an n 2 n
 11.1.16: an n n
 11.1.17: an 6n 3n2 1 a
 11.1.18: an 2n
 11.1.19: an 1 1n n
 11.1.20: an 1 1n an
 11.1.21: an 2 1 3n
 11.1.22: an 2n 3n
 11.1.23: an 1 n3 2
 11.1.24: an 10 n2 3
 11.1.25: an 1n n2
 11.1.26: an 1n n n 1 an
 11.1.27: an
 11.1.28: an 0.3
 11.1.29: a 2 6 n n n 1 n 2 an
 11.1.30: an n n a 2 6
 11.1.31: an 1n 1 n2 1 a
 11.1.32: an 1n
 11.1.33: a n n 1 n 1n 3n 2 an
 11.1.34: an 1n1 a n n 1 n
 11.1.35: an 4n 2n2 3
 11.1.36: an 4n2 n 3 n n 1 n 2 an
 11.1.37: an 2 3
 11.1.38: an 2 4 n a
 11.1.39: an 16 0.5n1 an
 11.1.40: an 8 0.75n
 11.1.41: an 2n n 1
 11.1.42: an 3n2 n2
 11.1.43: an 8 n 1
 11.1.44: an 8n n 1
 11.1.45: an 4 0.5n1
 11.1.46: an 4n n!
 11.1.47:
 11.1.48:
 11.1.49: 0, 3, 8, 15, 24, . . .
 11.1.50: 2, 4, 6, 8, 10, . . . 1
 11.1.51: , . . . 2 3, 3 4, 4 5, 5 6, 6 7, . . . 0,
 11.1.52: 2, 1 4, 1 8, 1 16 , . . . 2
 11.1.53: 2 1, 3 3, 4 5, 5 7, 6 9, . . .
 11.1.54: 1 3, 2 9, 4 27, 8 81, . . .
 11.1.55: 1, , . . . 1 4, 1 9, 1 16, 1 25, . . .
 11.1.56: 1, 1 2, 1 6, 1 24, 1 120 1, , . . .
 11.1.57: 1, 1, 1, 1, 1, . . . ,
 11.1.58: 1, 2, 22 2 , 23 6 , 24 24, 25 120
 11.1.59: 1, 3, 1, 3, 1, .
 11.1.60: 3, 3 2, 1, 3 4, 3 5
 11.1.61: 1 1 1, 1 1 2, 1 1 3, 1 1 4, 1 1 5, . . .
 11.1.62: 1 1 2, 1 3 4, 1 7 8, 1 15 16, 1 31 32, . . .
 11.1.63: a1 28, ak 1 ak 4
 11.1.64: a1 15, ak 1 ak 3
 11.1.65: a ak 1 2 ak 1 1
 11.1.66: a1 32, 2ak
 11.1.67: a1 6, ak 1 ak 2
 11.1.68: a1 25, ak 1 ak 5
 11.1.69: a1 81, 3ak
 11.1.70: a1 14, ak 1 2ak
 11.1.71: an 1 n!
 11.1.72: an n! 2n 1 a
 11.1.73: an 1 n 1!
 11.1.74: an n2 n 1!
 11.1.75: an 12n 2n! a
 11.1.76: an 12n 1 2n 1! a
 11.1.77: 4! 6!
 11.1.78: 5! 8!
 11.1.79: 12! 4! 8!
 11.1.80: 10! 3! 4! 6!
 11.1.81: n 1! n!
 11.1.82: n 2! n!
 11.1.83: 2n 1! 2n 1!
 11.1.84: 3n 1! 3n!
 11.1.85: 5 i1 2i 1
 11.1.86: 6 i1 3i 1
 11.1.87: 6 4 k1 10
 11.1.88: 5 k1 6
 11.1.89: 4 i0 i
 11.1.90: 5 i0 3i 2
 11.1.91: 2 3 3 k0 1 k2 1
 11.1.92: 5 j3 1 j 2 3
 11.1.93: 5 k2 k 12 k 3
 11.1.94: 4 i1 i 12 i 13 5 k2 k 12 k 3 5 j3 1 j 2 3 3
 11.1.95: 4 i1 2i
 11.1.96: 4 j0 2j
 11.1.97: 1 2n 1
 11.1.98: 3 j 1
 11.1.99: k! 4 k0 1k k 1
 11.1.100: 4 k0 1k k!
 11.1.101: 25 n0 1 4n
 11.1.102: 25 n0 1 5 n 1
 11.1.103: 3 1 1 3 2 1 3 3 . . . 1 3 9
 11.1.104: 5 1 1 5 1 2 5 1 3 . . . 5 1 15
 11.1.105: 2 1 8 3 2 2 8 3 . . . 2 8 8 3
 11.1.106: 1 1 6 2 1 2 6 2 . . . 1 6 6 2 2
 11.1.107: 3 9 27 81 243 729 1
 11.1.108: 1 1 2 1 4 1 8 . . . 1 128 3
 11.1.109: 12 1 22 1 32 1 42 . . . 1 202 1
 11.1.110: 1 3 1 2 4 1 3 5 . . . 1 10 12
 11.1.111: 1 4 3 8 7 16 15 32 31 64
 11.1.112: 2 2 4 6 8 24 16 120 32 720
 11.1.113: i1 5 1 2
 11.1.114: i1 2 1 3
 11.1.115: n1 4 1 2
 11.1.116: n1 8 1 4
 11.1.117: i1 6 1 10
 11.1.118: k1 1 10 k
 11.1.119: k1 7 1 10 k
 11.1.120: i1 2 1 10 i
 11.1.121: COMPOUND INTEREST You deposit $25,000 in an account that earns 7% i...
 11.1.122: COMPOUND INTEREST A deposit of $10,000 is made in an account that e...
 11.1.123: DATA ANALYSIS: NUMBER OF STORES The table shows the numbers of Best...
 11.1.124: MEDICINE The numbers (in thousands) of AIDS cases reported from 200...
 11.1.125: FEDERAL DEBT From 1995 to 2007, the federal debt of the United Stat...
 11.1.126: REVENUE The revenues (in millions of dollars) of Amazon.com from 20...
 11.1.127: 4 i1 i 2 2i 4 i1 i 2 2 4 i1 i
 11.1.128: 4 j1 2 j 6 j3 2 j2
 11.1.129: Write the first 12 terms of the Fibonacci sequence and the first 10...
 11.1.130: Using the definition for in Exercise 129, show that can be defined ...
 11.1.131: Find the arithmetic mean of the six checking account balances $327....
 11.1.132: Find the arithmetic mean of the following prices per gallon for reg...
 11.1.133: PROOF Prove that
 11.1.134: PROOF Prove that
 11.1.135: an xn n!
 11.1.136: an 1nx2n 1 2n 1 a
 11.1.137: an 1n x2n 2n! a
 11.1.138: an 1nx2n 1 2n 1!
 11.1.139: Write out the first five terms of the sequence whose term is Are th...
 11.1.140: CAPSTONE In your own words,
 11.1.141: A cube is created using 27 unit cubes (a unit cube has a length, wi...
Solutions for Chapter 11.1: Sequences and Series
Full solutions for Algebra and Trigonometry  8th Edition
ISBN: 9781439048474
Solutions for Chapter 11.1: Sequences and Series
Get Full SolutionsChapter 11.1: Sequences and Series includes 141 full stepbystep solutions. Since 141 problems in chapter 11.1: Sequences and Series have been answered, more than 51621 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: 9781439048474. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8.

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

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

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

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

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.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

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.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

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

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

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

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

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.