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Problem 19 Easy Difficulty

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

Answer

$\sum_{n=0}^{\infty}(2 n+1) x^{n}, \quad R=1$

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Video Transcript

find the power serious representation of a function and determine the readers of burdens. So after facts, because one person likes times the derivative of one over one minus X in terms that one. So let's see if it's crept. So one hour was X and everything is gonna be when you work. One one is just my woman's X square and like one here. So you have filtered into one. So this is true, okay? And we continue. We can expand this part so it becomes minus one minus X guns, sir. Zero from any from zero to infinity. An expert in And is it just knight to not to go from zero to open day expelled in minus stew and from zero to in any hour end class work and the fun the reserve burdens it requires absolute. That is less than one. Which place are equals. What? Okay,

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