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Problem 7 Easy Difficulty

Find a power series representation for the function and determine the interval of convergence.
$ f(x) = \frac {x^2}{x^4 + 16} $

Answer

$\sum_{n=0}^{\infty} \frac{(-1)^{n} x^{4 n+2}}{16^{n+1}}$

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Video Transcript

Okay, So we first gonna re white FX as X squared over sixteen times one or one class. That's the four over sixteen. And this is very familiar. It goes to with serious experience. I want this one to our inn succeded power and as a denominator and the right will be our foreign. And then it goes to this for Sean's. This one was for Oh, there's a mistake here. So this is here. This is square. So they're square And the readers of Convergence Thean they're welcome. Ernest will be after the four of sixteen. The model of it is less than one. So that implies the model of eggs is less then two.

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