Find a power series for the function centered at c and determine the interval of convergence.(adsbygoogle = window.adsbygoogle || []).push({});

c = 0

[tex]f(x)=\frac{2}{1-x^2}[/tex]

After some partial fractions work and getting the partials in the form of

[tex]\frac{a}{1-r}[/tex]

I have

[tex]\sum x^n + \sum(-x)^n[/tex]

if I factor out the x^n's I get

[tex]\sum(1+(-1)^n)x^n[/tex]

This is where I'm stuck, the solution manual shows it then going to

[tex]\sum2x^{2n}[/tex]

I've been staring at this thing for 15 mins and can't see how it's possible. Could someone give me a little push in the right direction with this? Thanks.

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# Homework Help: Adding geometric series

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