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Determine whether the following series converges. 4(-1)k 2k +9 k=0 OB. The series diverges because ak = OC. The series diverges because ak = ak+1 ≤ak- O D. The series converges because ak = OE. The series converges because ak = ak+1 ≤ak. OF. The series diverges because ak is nonincreasing in magnitude for k greater than some index N and lim a = k→∞ and for any index N, there are some values of k>N for which ak+12ak and some values of k> N for which is nonincreasing in magnitude for k greater than some index N and lim a = k→∞ and for any index N, there are some values of k> N for which ak+12ak and some values of k> N for which is nondecreasing in magnitude for k greater than some index N.

Determine whether the following series converges. 4(-1)k 2k +9 k=0 OB. The series diverges because ak = OC. The series diverges because ak = ak+1 ≤ak- O D. The series converges because ak = OE. The series converges because ak = ak+1 ≤ak. OF. The series diverges because ak is nonincreasing in magnitude for k greater than some index N and lim a = k→∞ and for any index N, there are some values of k>N for which ak+12ak and some values of k> N for which is nonincreasing in magnitude for k greater than some index N and lim a = k→∞ and for any index N, there are some values of k> N for which ak+12ak and some values of k> N for which is nondecreasing in magnitude for k greater than some index N.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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Determine whether the following series converges. 4(-1)k Σ 2k+9 k=0 Let ak > 0 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 converges because ak = B. The series diverges because ak = OC. The series diverges because ak = ak+1 ≤ak. D. The series converges because ak E. nuoraos ho The corios con 11 ... is nondecreasing in magnitude for k greater than some index N. is nonincreasing in magnitude for k greater than some index N and lim ak = k→∞ and for any index N, there are some values of k> N for which ak +12 ak and some values of k> N for which is nonincreasing in magnitude for k greater than some index N and lim k→∞ and for any indov N there are come values of kN for which a ak = 0. and come values of N for which
Transcribed Image Text:Determine whether the following series converges. 4(-1)k Σ 2k+9 k=0 Let ak > 0 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 converges because ak = B. The series diverges because ak = OC. The series diverges because ak = ak+1 ≤ak. D. The series converges because ak E. nuoraos ho The corios con 11 ... is nondecreasing in magnitude for k greater than some index N. is nonincreasing in magnitude for k greater than some index N and lim ak = k→∞ and for any index N, there are some values of k> N for which ak +12 ak and some values of k> N for which is nonincreasing in magnitude for k greater than some index N and lim k→∞ and for any indov N there are come values of kN for which a ak = 0. and come values of N for which
Determine whether the following series converges. 4(-1)k 2k+9 Σ k=0 B. The series diverges because ak = = OC. The series diverges because ak ak+1 ≤ak. D. The series converges because ak = is nonincreasing in magnitude for k greater than some index N and lim a₁ = k→∞ 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→∞ and for any index N, there are some values of k> N for which ak+12ak and some values of k> N for which OE. The series converges because ak = ak+1 ≤ak. OF. The series diverges because ak = is nondecreasing in magnitude for k greater than some index N.
Transcribed Image Text:Determine whether the following series converges. 4(-1)k 2k+9 Σ k=0 B. The series diverges because ak = = OC. The series diverges because ak ak+1 ≤ak. D. The series converges because ak = is nonincreasing in magnitude for k greater than some index N and lim a₁ = k→∞ 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→∞ and for any index N, there are some values of k> N for which ak+12ak and some values of k> N for which OE. The series converges because ak = ak+1 ≤ak. OF. The series diverges because ak = is nondecreasing in magnitude for k greater than some index N.
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