Use the power series for f(x) = 1/(1-x) to write the function g(x) = x^2/(2 - x^2) as a power series. write your answer as a summation with a lower index of n = 0, and simplify the summation to a single variable.
would really appreciate the

Since



for , the power series for the rightmost rational expression is



which is applicable for , or .

Distributing the other rational expression gives



I'm not sure what is meant by "simplify the summation to a single variable", but you can rewrite this as



which could be interpreted as a simpler form, but that's really in the eye of the beholder...

Okay so it will be 1123