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Determine whether the following series converges. k 11k 5+1 Σ (-1)k+1. k=1 Let ak 20 represent the magnitude of the terms of the given series. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The series diverges because ak is nondecreasing in magnitude for k greater than some index N. OB. The series diverges because ak is nonincreasing in magnitude for k greater than some index N and lim ak = k→∞ O C. The series converges because for any index N, there are some values of k> N for which ak + 1 ≥ak and some values of k> N for which ak+1 ≤ak. O D. The series converges because ak is nonincreasing in magnitude for k greater than some index N and lim ak = k→∞ O E. The series diverges because for any index N, there are some values of k> N for which ak + 1 ≥ak and some values of k>N for which ak+1 ≤ak. OF. The series converges because a is nondecreasing in magnitude for k greater than some index N.

Determine whether the following series converges. k 11k 5+1 Σ (-1)k+1. k=1 Let ak 20 represent the magnitude of the terms of the given series. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The series diverges because ak is nondecreasing in magnitude for k greater than some index N. OB. The series diverges because ak is nonincreasing in magnitude for k greater than some index N and lim ak = k→∞ O C. The series converges because for any index N, there are some values of k> N for which ak + 1 ≥ak and some values of k> N for which ak+1 ≤ak. O D. The series converges because ak is nonincreasing in magnitude for k greater than some index N and lim ak = k→∞ O E. The series diverges because for any index N, there are some values of k> N for which ak + 1 ≥ak and some values of k>N for which ak+1 ≤ak. OF. The series converges because a is nondecreasing in magnitude for k greater than some index N.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Determine whether the following series converges. ∞ k Σ (-1)k+1. . 5 k=1 11k + 1 Let ak 20 represent the magnitude of the terms of the given series. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The series diverges because ak is nondecreasing in magnitude for k greater than some index N. B. The series diverges because ak is nonincreasing in magnitude for k greater than some index N and lim ak = k→∞ sak. O C. The series converges because for any index N, there are some values of k>N for which ak+ 1 ≥ak and some values of k > N for which ak + 1 k→∞ D. The series converges because ak is nonincreasing in magnitude for k greater than some index N and lim ak = sak. O E. The series diverges because for any index N, there are some values of k> N for which ak+ 1 ≥ak and some values of k> N for which ak + 1 O F. The series converges because ak is nondecreasing in magnitude for k greater than some index N.
Transcribed Image Text:Determine whether the following series converges. ∞ k Σ (-1)k+1. . 5 k=1 11k + 1 Let ak 20 represent the magnitude of the terms of the given series. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The series diverges because ak is nondecreasing in magnitude for k greater than some index N. B. The series diverges because ak is nonincreasing in magnitude for k greater than some index N and lim ak = k→∞ sak. O C. The series converges because for any index N, there are some values of k>N for which ak+ 1 ≥ak and some values of k > N for which ak + 1 k→∞ D. The series converges because ak is nonincreasing in magnitude for k greater than some index N and lim ak = sak. O E. The series diverges because for any index N, there are some values of k> N for which ak+ 1 ≥ak and some values of k> N for which ak + 1 O F. The series converges because ak is nondecreasing in magnitude for k greater than some index N.
Determine whether the following series converges. 9(-1)k +8 ∞ k=0 Let ak 20 represent the magnitude of the terms of the given series. Select the correct choice below and fill in the answer box(es) to complete your choice. A. The series diverges because ak = ak+1 ≤ak. OB. The series diverges because ak = OC. The series converges because ak ak+1 ≤ak. OD. The series converges because ak O E. The series diverges because ak = O F. The series converges because ak = = and for any index N, there are some values of k> N for which ak + 1 ≥ak and some values of k> N for which is nondecreasing in magnitude for k greater than some index N. and for any index N, there are some values of k> N for which ak + 1 ≥ak and some values of k > N for which is nonincreasing in magnitude for k greater than some index N and lim ak = k→∞ is nonincreasing in magnitude for k greater than some index N and lim ak k→∞ is nondecreasing in magnitude for k greater than some index N.
Transcribed Image Text:Determine whether the following series converges. 9(-1)k +8 ∞ k=0 Let ak 20 represent the magnitude of the terms of the given series. Select the correct choice below and fill in the answer box(es) to complete your choice. A. The series diverges because ak = ak+1 ≤ak. OB. The series diverges because ak = OC. The series converges because ak ak+1 ≤ak. OD. The series converges because ak O E. The series diverges because ak = O F. The series converges because ak = = and for any index N, there are some values of k> N for which ak + 1 ≥ak and some values of k> N for which is nondecreasing in magnitude for k greater than some index N. and for any index N, there are some values of k> N for which ak + 1 ≥ak and some values of k > N for which is nonincreasing in magnitude for k greater than some index N and lim ak = k→∞ is nonincreasing in magnitude for k greater than some index N and lim ak k→∞ is nondecreasing in magnitude for k greater than some index N.
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