Find the radii of convergence for each of the following power series. (a) n=1 n(x - 1)" 2n
Find the radii of convergence for each of the following power series. (a) n=1 n(x - 1)" 2n
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:Find the radii of convergence for each of the following power series.
(a)
(b)
(c)
n=1
n(x - 1)"
2n
(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
(1+1)* S.M.
≤n.
n=2
(x - π)"
n(n − 1)*
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