Use the Alternating Series Test to determine whether the series converges. k E(- 1)k+1 3k° + 1 k= 1 Let a represent the magnitude of the terms of the given series and f(x) be the function that generates a. Determine whether the terms of the series are nonincreasing in magnitude. Select the correct choice below and fill in the answer box in your choice. O A. The terms of the series are nonincreasing in magnitude. Since f'(x) = 1 < 0 for x> 6. 15 the terms a, decrease for k21. %3D OB. 1 > 0 for x> The terms of the series are increasing in magnitude. Since f'(x) = the terms a increase fork21. 6 15

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question

4

Use the Alternating Series Test to determine whether the series converges.
k
E(- 1)k+1
3k° + 1
k= 1
Let a represent the magnitude of the terms of the given series and f(x) be the function that generates a. Determine whether the terms
of the series are nonincreasing in magnitude.
Select the correct choice below and fill in the answer box in your choice.
O A.
The terms of the series are nonincreasing in magnitude. Since f'(x) =
1
< 0 for x>
6.
15
the terms a,
decrease for k21.
%3D
OB.
1
> 0 for x>
The terms of the series are increasing in magnitude. Since f'(x) =
the terms a increase fork21.
6 15
Transcribed Image Text:Use the Alternating Series Test to determine whether the series converges. k E(- 1)k+1 3k° + 1 k= 1 Let a represent the magnitude of the terms of the given series and f(x) be the function that generates a. Determine whether the terms of the series are nonincreasing in magnitude. Select the correct choice below and fill in the answer box in your choice. O A. The terms of the series are nonincreasing in magnitude. Since f'(x) = 1 < 0 for x> 6. 15 the terms a, decrease for k21. %3D OB. 1 > 0 for x> The terms of the series are increasing in magnitude. Since f'(x) = the terms a increase fork21. 6 15
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