Hey,

The question ask you to find all values of x for which the series converges. For these values of x, write the sum of the series as a function of x.

$\displaystyle \displaystyle\large\sum\limits^\infty_{n=0}(-1)^{n}x^{2n}$

It is alternating, so if the ratio is r = -x^2 then -x^2 must be less than 1 to converge, and if it r = x^2 then x^2 must be less than 1 to converge.

This is where I got lost. It seems i'll have 2 different answers. How would I be able to come up with the sum of the series as a function afterward?

Help?