I have another function $\displaystyle \frac{1}{1+25x^2}$ wich I have to represent as as a power series $\displaystyle f(x) = \sum_{n=0}^{\infty} c_nx^n$

it seems to me that I got something different because the coefficients I get are not correct.

what I got is $\displaystyle f(x) = \sum_{n=0}^{\infty} (-25)^{n}x^{2n}$ with a Radius of convergence R= 1/5

the first few coefficients I get are $\displaystyle 1-25+25^{2}-25^{3}+25^{4} $

I know that my radius of convergence is correct, but I can't understand where is my mistake with the coefficients,

thank you