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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
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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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)*
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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