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Determine whether the following series converges. 00 In k k= 1

Determine whether the following series converges. 00 In k k= 1

Advanced Engineering Mathematics
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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Determine whether the following series converges. 2-1)k+1 In k k = 1 Let ak >U represent the magnitude of the terms of the given series. Identify and describe a. Select the correct choice below and fill in any answer box in your choice. O A. The series diverges because ak is nonincreasing in magnitude for k greater than some index N and lim a O B. The series converges because ak = and for index N, there are some values of k> N for which a1 za, and some values of k>N for which a+1sak. %3D any O C. The series converges because ak = is nonincreasing in magnitude for k greater than some index N and lim a O D. The series diverges because ak = sak and for any index N, there are some values of k> N for which a, ,2 ar and some values of k> N for which ar 1 O E. The series converges because ak = is nondecreasing in magnitude for k greater than some index N. O F. The series diverges because ak = is nondecreasing in magnitude for k greater than some index N. %3D 1°C 1+61 Mostly cloudy 121 PrUB ma iss ve B.
Transcribed Image Text:Determine whether the following series converges. 2-1)k+1 In k k = 1 Let ak >U represent the magnitude of the terms of the given series. Identify and describe a. Select the correct choice below and fill in any answer box in your choice. O A. The series diverges because ak is nonincreasing in magnitude for k greater than some index N and lim a O B. The series converges because ak = and for index N, there are some values of k> N for which a1 za, and some values of k>N for which a+1sak. %3D any O C. The series converges because ak = is nonincreasing in magnitude for k greater than some index N and lim a O D. The series diverges because ak = sak and for any index N, there are some values of k> N for which a, ,2 ar and some values of k> N for which ar 1 O E. The series converges because ak = is nondecreasing in magnitude for k greater than some index N. O F. The series diverges because ak = is nondecreasing in magnitude for k greater than some index N. %3D 1°C 1+61 Mostly cloudy 121 PrUB ma iss ve B.
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