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Problem 20 Easy Difficulty

Find a power series representation for the function and determine the radius of convergence.
$ f(x) = \frac {x^2 + x}{(1 - x)^3} $

Answer

$f(x)=\sum_{n=0}^{\infty} \left(\frac{n+2}{n}\right)x^{n+2}+\sum_{n=0}^{\infty}\left(\frac{n+2}{n}\right) x^{n+1}$
$R=1$

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Video Transcript

please. Yeah. Okay. So find the power serious reputation for the function and determine the raiders Convergence. So at that sequels X squared plus x times, the sea jets and Drea s equals one or women's X cube. And we got first expand GS and the expanding equals two from zero to infinity. That CDO the infamous extra power vent and the equations by the binomial theorem is going to be one plus three minus in class three, minus one or over and minus one. No, this over in. Yes. So this is going to be in from zero to infinity and plus two who is in Tom's asked to power in and we plug in Jack's into the equation one. So the fundraise off after Pat's he's going to be and, hey, signal from zero to infinity. And that's to choose in extra power and plus two class and from zero to infinity, the interest to over in absolute heart and plus one and the readers convergence is gonna be Are you close? One

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