 9.4.1: What is an nth partial sum?
 9.4.2: What is the difference between an arithmetic sequence and an arithm...
 9.4.3: What is a geometric series?
 9.4.4: How is finding the sum of an infinite geometric series different fr...
 9.4.5: What is an annuity?
 9.4.6: For the following exercises, express each description of a sum usin...
 9.4.7: For the following exercises, express each description of a sum usin...
 9.4.8: For the following exercises, express each description of a sum usin...
 9.4.9: For the following exercises, express each description of a sum usin...
 9.4.10: For the following exercises, express each arithmetic sum using summ...
 9.4.11: For the following exercises, express each arithmetic sum using summ...
 9.4.12: For the following exercises, express each arithmetic sum using summ...
 9.4.13: For the following exercises, use the formula for the sum of the fir...
 9.4.14: For the following exercises, use the formula for the sum of the fir...
 9.4.15: For the following exercises, use the formula for the sum of the fir...
 9.4.16: For the following exercises, express each geometric sum using summa...
 9.4.17: For the following exercises, express each geometric sum using summa...
 9.4.18: For the following exercises, express each geometric sum using summa...
 9.4.19: For the following exercises, use the formula for the sum of the fir...
 9.4.20: For the following exercises, use the formula for the sum of the fir...
 9.4.21: For the following exercises, use the formula for the sum of the fir...
 9.4.22: For the following exercises, determine whether the infinite series ...
 9.4.23: For the following exercises, determine whether the infinite series ...
 9.4.24: For the following exercises, determine whether the infinite series ...
 9.4.25: For the following exercises, determine whether the infinite series ...
 9.4.26: For the following exercises, use the following scenario. Javier mak...
 9.4.27: For the following exercises, use the following scenario. Javier mak...
 9.4.28: For the following exercises, use the geometric series k = 1 1 __ 2 ...
 9.4.29: For the following exercises, use the geometric series k = 1 1 __ 2 ...
 9.4.30: For the following exercises, find the indicated sum. . a = 1 14 a
 9.4.31: For the following exercises, find the indicated sum. n = 1 6 n(n 2)
 9.4.32: For the following exercises, find the indicated sum. k = 1 17 k2
 9.4.33: For the following exercises, find the indicated sum. k = 1 7 2k
 9.4.34: For the following exercises, use the formula for the sum of the fir...
 9.4.35: For the following exercises, use the formula for the sum of the fir...
 9.4.36: For the following exercises, use the formula for the sum of the fir...
 9.4.37: For the following exercises, use the formula for the sum of the fir...
 9.4.38: For the following exercises, use the formula for the sum of the fir...
 9.4.39: For the following exercises, use the formula for the sum of the fir...
 9.4.40: For the following exercises, use the formula for the sum of the fir...
 9.4.41: For the following exercises, use the formula for the sum of the fir...
 9.4.42: For the following exercises, find the sum of the infinite geometric...
 9.4.43: For the following exercises, find the sum of the infinite geometric...
 9.4.44: For the following exercises, find the sum of the infinite geometric...
 9.4.45: For the following exercises, find the sum of the infinite geometric...
 9.4.46: For the following exercises, determine the value of the annuity for...
 9.4.47: For the following exercises, determine the value of the annuity for...
 9.4.48: For the following exercises, determine the value of the annuity for...
 9.4.49: For the following exercises, determine the value of the annuity for...
 9.4.50: The sum of terms 50 k 2 from k = x through 7 is 115. What is x?
 9.4.51: Write an explicit formula for ak such that k = 0 6 ak = 189 . Assum...
 9.4.52: Find the smallest value of n such that k = 1 n (3k 5) > 100 .
 9.4.53: How many terms must be added before the series 1 3 5 7.... has a su...
 9.4.54: Write 0. _ 65 as an infinite geometric series using summation notat...
 9.4.55: The sum of an infinite geometric series is five times the value of ...
 9.4.56: To get the best loan rates available, the Riches want to save enoug...
 9.4.57: Karl has two years to save $10,000 to buy a used car when he gradua...
 9.4.58: Keisha devised a weeklong study plan to prepare for finals. On the...
 9.4.59: A boulder rolled down a mountain, traveling 6feet in the first seco...
 9.4.60: A scientist places 50 cells in a petri dish. Every hour, the popula...
 9.4.61: A pendulum travels a distance of 3 feet on its first swing. On each...
 9.4.62: Rachael deposits $1,500 into a retirement fund each year. The fund ...
Solutions for Chapter 9.4: SERIES AND THEIR NOTATIONS
Full solutions for College Algebra  1st Edition
ISBN: 9781938168383
Solutions for Chapter 9.4: SERIES AND THEIR NOTATIONS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 9.4: SERIES AND THEIR NOTATIONS includes 62 full stepbystep solutions. Since 62 problems in chapter 9.4: SERIES AND THEIR NOTATIONS have been answered, more than 30186 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra, edition: 1. College Algebra was written by and is associated to the ISBN: 9781938168383.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

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).

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

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

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

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

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.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

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

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

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

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

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.

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).

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

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.