 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 26034 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.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

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.

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

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.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

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.

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

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

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).

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.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Solvable system Ax = b.
The right side b is in the column space of A.

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

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

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.

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