I need to analyze the series $\sum_{n=0}^\infty{x^n\cos(\frac{n\pi}{2})}$, and I have already shown that it converges. Now I am trying to find the sum, and I noticed that $\cos(\frac{n\pi}{2})$ gives a sequence ${1; 0; -1; 0; 1;...}$, but how do I find the general term of this sequence generated by the $\cos$ to find the sum?
I am still new to series, so far I am trying to transform the series into a sum of terms of a geometric progression. Is there any other way to do it easily?