Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
Find the radii of convergence for each of the following power series.
(2)
n=1
n(− 1)"
2n
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Transcribed Image Text:Find the radii of convergence for each of the following power series. (2) n=1 n(− 1)" 2n
(b)
(c)
Σ(n= − 1)x",
n=1
Hint: The radius of convergence is 1. Explain why you can show
this by checking that the series converges for x = -1, but diverges
for x = 1. To show the latter, it is helpful to recall that
n=2
n
≤n.
(x - π)"
n(n-1)*
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Transcribed Image Text:(b) (c) Σ(n= − 1)x", n=1 Hint: The radius of convergence is 1. Explain why you can show this by checking that the series converges for x = -1, but diverges for x = 1. To show the latter, it is helpful to recall that n=2 n ≤n. (x - π)" n(n-1)*
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