 Chapter 11.1: In Exercises 14, write the first four terms of each sequence whose ...
 Chapter 11.2: In Exercises 14, write the first four terms of each sequence whose ...
 Chapter 11.3: In Exercises 14, write the first four terms of each sequence whose ...
 Chapter 11.4: In Exercises 14, write the first four terms of each sequence whose ...
 Chapter 11.5: In Exercises 56, find each indicated sum.a5i=1(2i2  3)
 Chapter 11.6: In Exercises 56, find each indicated sum.a4i=0(1)i+1i!
 Chapter 11.7: In Exercises 78, express each sum using summation notation. Use i f...
 Chapter 11.8: In Exercises 78, express each sum using summation notation. Use i f...
 Chapter 11.9: In Exercises 911, write the first six terms of each arithmetic sequ...
 Chapter 11.10: In Exercises 911, write the first six terms of each arithmetic sequ...
 Chapter 11.11: In Exercises 911, write the first six terms of each arithmetic sequ...
 Chapter 11.12: In Exercises 1214, use the formula for the general term (the nth te...
 Chapter 11.13: In Exercises 1214, use the formula for the general term (the nth te...
 Chapter 11.14: In Exercises 1214, use the formula for the general term (the nth te...
 Chapter 11.15: In Exercises 1518, write a formula for the general term (the nth te...
 Chapter 11.16: In Exercises 1518, write a formula for the general term (the nth te...
 Chapter 11.17: In Exercises 1518, write a formula for the general term (the nth te...
 Chapter 11.18: In Exercises 1518, write a formula for the general term (the nth te...
 Chapter 11.19: Find the sum of the first 22 terms of the arithmetic sequence: 5, 1...
 Chapter 11.20: Find the sum of the first 15 terms of the arithmetic sequence: 6, ...
 Chapter 11.21: Find 3 + 6 + 9 + g + 300, the sum of the first 100 positive multipl...
 Chapter 11.22: In Exercises 2224, use the formula for the sum of the first n terms...
 Chapter 11.23: In Exercises 2224, use the formula for the sum of the first n terms...
 Chapter 11.24: In Exercises 2224, use the formula for the sum of the first n terms...
 Chapter 11.25: The graphic indicates that there are more eyes at school. 2005 58% ...
 Chapter 11.26: A company offers a starting salary of $31,500 with raises of $2300 ...
 Chapter 11.27: A theater has 25 seats in the first row and 35 rows in all. Each su...
 Chapter 11.28: In Exercises 2831, write the first five terms of each geometric seq...
 Chapter 11.29: In Exercises 2831, write the first five terms of each geometric seq...
 Chapter 11.30: In Exercises 2831, write the first five terms of each geometric seq...
 Chapter 11.31: In Exercises 2831, write the first five terms of each geometric seq...
 Chapter 11.32: In Exercises 3234, use the formula for the general term (the nth te...
 Chapter 11.33: In Exercises 3234, use the formula for the general term (the nth te...
 Chapter 11.34: In Exercises 3234, use the formula for the general term (the nth te...
 Chapter 11.35: In Exercises 3537, write a formula for the general term (the nth te...
 Chapter 11.36: In Exercises 3537, write a formula for the general term (the nth te...
 Chapter 11.37: In Exercises 3537, write a formula for the general term (the nth te...
 Chapter 11.38: Find the sum of the first 15 terms of the geometric sequence: 5, 1...
 Chapter 11.39: Find the sum of the first 7 terms of the geometric sequence: 8, 4, ...
 Chapter 11.40: In Exercises 4042, use the formula for the sum of the first n terms...
 Chapter 11.41: In Exercises 4042, use the formula for the sum of the first n terms...
 Chapter 11.42: In Exercises 4042, use the formula for the sum of the first n terms...
 Chapter 11.43: In Exercises 4346, find the sum of each infinite geometric series.9...
 Chapter 11.44: In Exercises 4346, find the sum of each infinite geometric series.2...
 Chapter 11.45: In Exercises 4346, find the sum of each infinite geometric series....
 Chapter 11.46: In Exercises 4346, find the sum of each infinite geometric series.....
 Chapter 11.47: In Exercises 4748, express each repeating decimal as a fraction in ...
 Chapter 11.48: In Exercises 4748, express each repeating decimal as a fraction in ...
 Chapter 11.49: Projections for the U.S. population, ages 85 and older, are shown i...
 Chapter 11.50: A job pays $32,000 for the first year with an annual increase of 6%...
 Chapter 11.51: In Exercises 5152, use the formula for the value of an annuity and ...
 Chapter 11.52: In Exercises 5152, use the formula for the value of an annuity and ...
 Chapter 11.53: A factory in an isolated town has an annual payroll of $4 million. ...
 Chapter 11.54: In Exercises 5455, evaluate the given binomial coefficient.118
 Chapter 11.55: In Exercises 5455, evaluate the given binomial coefficient.902
 Chapter 11.56: In Exercises 5659, use the Binomial Theorem to expand each binomial...
 Chapter 11.57: In Exercises 5659, use the Binomial Theorem to expand each binomial...
 Chapter 11.58: In Exercises 5659, use the Binomial Theorem to expand each binomial...
 Chapter 11.59: In Exercises 5659, use the Binomial Theorem to expand each binomial...
 Chapter 11.60: In Exercises 6061, write the first three terms in each binomial exp...
 Chapter 11.61: In Exercises 6061, write the first three terms in each binomial exp...
 Chapter 11.62: In Exercises 6263, find the indicated term in each expansion.. (x +...
 Chapter 11.63: In Exercises 6263, find the indicated term in each expansion.(2x  ...
Solutions for Chapter Chapter 11: Sequences, Series, and the Binomial Theorem
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter Chapter 11: Sequences, Series, and the Binomial Theorem
Get Full SolutionsThis textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. Chapter Chapter 11: Sequences, Series, and the Binomial Theorem includes 63 full stepbystep solutions. Since 63 problems in chapter Chapter 11: Sequences, Series, and the Binomial Theorem have been answered, more than 9666 students have viewed full stepbystep solutions from this chapter. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. This expansive textbook survival guide covers the following chapters and their solutions.

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

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

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].

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

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.

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.

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

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.

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

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 •

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).

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

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

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

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