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Problem 17 Medium Difficulty

Find a power series representation for the function and determine the radius of convergence.
$ f(x) = \frac {x}{(1 + 4x)^2} $

Answer

$\sum_{n=0}^{\infty}(-1)^{n+1} 4^{n-1} x^{n+1}$
$R=\frac{1}{4}$

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Video Transcript

Okay, So find a power source. Reputation function and determine the rapist from murders. That's it Goes eggs over cue. The square of one has warrants. So how do we suppose to spend this? Okay, we can do the technic. So basically, this is next. You one horse comes to do with the one word with us for X. So a status. It is true. Well, this is the reality of what, One hour with the spreads. This is just one of you are not the one who are with us for X squared times for services once more, or one of us for a square. And here we have better. When we were for one horse Oh, he finds it out. So this is shoot. Okay, so then things becomes easier. We can just expand this part that is in from zero to infinity. Mine is looking forward to part in an extra hour. So on, Actually, we can We published part into this this old and it becomes too from zero to very on minus four. Okay, minus one to the power plus one, four two. Health on minus one and exited off plus one. Yes. So this the power Siri's and funded with this convergence. So happen here because we expanded from here and we require money. Sport X is from zero to one is from my neck. You want one? So that wass as is from nephew one fourth to one fourth. That is thing, Regis Convergence. Our Equus went forth.

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