Image attached, thanks Given that $ \frac{1}{1-x} = \sum_{n=0}^{\infty} x^n $ with convergence in $(-1, 1)$, find the power series for $ \frac{1}{1 + 2x^8} $ with center 0.\[\sum_{n=0}^{\infty}\] \[ \text{Identify its interval of convergence.} \]$ x = $ (Note: The solution should involve rewriting the expression $ \frac{1}{1 + 2x^8} $ as a geometric series and determining its interval of convergence.)

Given that 11-x=∑n=0∞xn with convergence in-1,1 .

Answered: 1 a" with convergence in (-1, 1), find…

1 a" with convergence in (-1, 1), find the power series for Given that with center 1+ 2x8 0. Identify its interval of convergence.

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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Image attached, thanks

Given that $ \frac{1}{1-x} = \sum_{n=0}^{\infty} x^n $ with convergence in $(-1, 1)$, find the power series for $ \frac{1}{1 + 2x^8} $ with center 0.

\[
\sum_{n=0}^{\infty}\]

\[ \text{Identify its interval of convergence.} \]

$ x = $

(Note: The solution should involve rewriting the expression $ \frac{1}{1 + 2x^8} $ as a geometric series and determining its interval of convergence.)

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