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Q. 61

Expert-verifiedFound in: Page 671

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

Let $\sum _{k=0}^{\mathrm{\infty}}\u200a{a}_{k}{x}^{k}$ be a power series in $x$ with a finite radius of convergence $p$. Prove that if the series converges absolutely at either $\pm p$, then the series converges absolutely at the other value as well.

Ans:

given,

$\sum _{k=0}^{\mathrm{\infty}}\u200a{a}_{k}{x}^{k}$

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