Math Challenges

\[ \displaylines{\text{a) }\sum_{k=1}^{\infty}\cos\left(\left(2k+1\right)\frac{\pi}{2}\right)\\ \text{b) }\sum_{k=1}^{\infty}\frac{4^{k-1}}{5^{k}}\\ \text{c) }\sum_{k=1}^{\infty}\frac{3^{k}}{2^{k}}} \]