Problem

Find a power series representation for the functi…

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Problem 8 Easy Difficulty

Find a power series representation for the function and determine the interval of convergence.
$ f(x) = \frac {x}{2x^2 + 1} $

Answer

$=\sum_{n=0}^{\infty}(-1)^{n} \cdot 2^{n} \cdot x^{n+1}$

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 9

Representations of Functions as Power Series

Discussion

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Video Transcript

So first, where the religious form as X comes one you are one of us, for this is one minus negative. Teo at square. And it goes to the barrier from their power. Siri's so minus two minus two to the power of and X to the power of to in and we just that s goes in it. So it goes to zero from there and from zero to infinity minus one too powerful. And I'm student health end times X to the power to end this way. And the in the well of convergence is being this. So then cries the absolute value of axes less than square a tive too. I start to over to sue them. Is thie. In a way, it was gonna be this.

Yiming Z.

University of Illinois at Urbana-Champaign