Suppose we are given a power series centered at 0 Σ Anx". n=0 153 n2 what's the radius of convergence R? If R is not +∞, is the series convergent at x = R, ) If an - R? and is it convergent at x = Come up with a power series (not necessarily centered at 0) that converges only at x = 153 but diverges elsewhere, and the sum of the seires at x = 153 is 153. Use computations to back up your answer

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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Suppose we are given a power series centered at 0
Σ
Anx".
n=0
153
n2
what's the radius of convergence R? If R is not +∞, is the series convergent at x = R,
) If an
- R?
and is it convergent at x =
Come up with a power series (not necessarily centered at 0) that converges only at x = 153 but
diverges elsewhere, and the sum of the seires at x = 153 is 153. Use computations to back up your
answer
Transcribed Image Text:Suppose we are given a power series centered at 0 Σ Anx". n=0 153 n2 what's the radius of convergence R? If R is not +∞, is the series convergent at x = R, ) If an - R? and is it convergent at x = Come up with a power series (not necessarily centered at 0) that converges only at x = 153 but diverges elsewhere, and the sum of the seires at x = 153 is 153. Use computations to back up your answer
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