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**calc101** Question:

Find a power series representation for the function and determine the interval of convergence:

$\displaystyle f(x) = \frac {1+x^2}{1-x^2}$

My attempt:

we know that

$\displaystyle \frac{1}{1-x} = \sum_{n=0}^{\infty} x^n $

Therefore,

$\displaystyle \frac{1}{1-x^2} = \sum x^{2n}$ (**)

Now, if we multiply by $\displaystyle x^2$ we get:

$\displaystyle \frac{x^2}{1-x^2} = \sum x^{4n}$

Then we add: $\displaystyle \frac{1}{1-x^2} $

So, $\displaystyle \sum_{n=0}^{\infty} x^{2n} + x^{4n}$

Am I correct?