 Appendix B.1: If a sequence 5sn6 converges to L, we call L the of the sequence.
 Appendix B.2: If a1, a2, p , an, p is some collection of numbers, the expression ...
 Appendix B.3: If the sequence 5Sn6 of partial sums of an infinite series a k=1 ak...
 Appendix B.4: If the sequence 5Sn6 of partial sums of an infinite series a k=1 ak...
 Appendix B.5: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.6: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.7: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.8: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.9: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.10: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.11: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.12: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.13: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.14: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.15: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.16: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.17: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.18: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.19: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.20: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.21: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.22: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.23: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.24: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.25: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.26: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.27: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.28: In 528, determine whether each sequence converges or diverges. If i...
 Appendix B.29: In 2932, find the first five terms in the sequence of partial sums ...
 Appendix B.30: In 2932, find the first five terms in the sequence of partial sums ...
 Appendix B.31: In 2932, find the first five terms in the sequence of partial sums ...
 Appendix B.32: In 2932, find the first five terms in the sequence of partial sums ...
Solutions for Chapter Appendix B: The Limit of a Sequence; Infinite Series
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter Appendix B: The Limit of a Sequence; Infinite Series
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter Appendix B: The Limit of a Sequence; Infinite Series includes 32 full stepbystep solutions. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. Since 32 problems in chapter Appendix B: The Limit of a Sequence; Infinite Series have been answered, more than 56643 students have viewed full stepbystep solutions from this chapter. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

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).

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

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!).

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.

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.

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.

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.

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).

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

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.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

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).

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

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.