How can I create a power series expansion for x^2 / (1+x^2)?

[yayMath]

I was wondering how to create a power series expansion for the function
x^2 / (1+x^2)... I've tried using the geometric series, but somehow i got stuck.
thanks.

 

[shmoe]

Geometric series should work fine. How about you post your work?

An alternate method: if you know the series for arctan(x), you can use the fact that it's derivative is 1/(1+x^2).

 

[philosophking]

It may also help you to think in what form geometric series are usually in, i.e.

1/(1-r). So maybe altering your fraction a bit will help you notice it.