Determine whether the following series converges. 00 k + 3k° +9 k+ 1 k (k?7 + 9) k = 1 ..... Let a >0 represent the magnitude of the terms of the given series. Identify and describe a. ak = |(Type an expression using k as the variable.) Determine if a is increasing in magnitude for k greater than some index N, is nonincreasing in magnitude for k greater than some index N, or neither. Recall that the terms of a series are nonincreasing in magnitude if 0
Determine whether the following series converges. 00 k + 3k° +9 k+ 1 k (k?7 + 9) k = 1 ..... Let a >0 represent the magnitude of the terms of the given series. Identify and describe a. ak = |(Type an expression using k as the variable.) Determine if a is increasing in magnitude for k greater than some index N, is nonincreasing in magnitude for k greater than some index N, or neither. Recall that the terms of a series are nonincreasing in magnitude if 0
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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Transcribed Image Text:Determine whether the following series converges.
00
18
9
E (- 1)k +1 k
k(k7 + 9)
+ 3k° + 9
k= 1
.....
Let a >0 represent the magnitude of the terms of the given series. Identify and describe a.
ak
(Type an expression using k as the variable.)
%3D
Determine if a is increasing in magnitude for k greater than some index N, is nonincreasing in magnitude for k greater than
some index N, or neither. Recall that the terms of a series are nonincreasing in magnitude if 0< ak+ 1<ak for k greater than
some index N. Select the correct choice below.
A. ak is increasing in magnitude for k greater than some index N.
B. ak is neither increasing nor nonincreasing in magnitude for k greater than some index N.
C. ak is nonincreasing in magnitude for k greater than some index N.
lim ak =
Does the series converge?
No
Yes
Click to select your answer(s).
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