$\displaystyle \sum_{n=0}^{\infty}(\frac{x}{2})^{2n+1}$
Not sure how to go abou this..
Any help?
$\displaystyle \sum_{n=0}^{\infty}\left(\frac{x^2}{4}\right)^{n}$ is a geometric series (common ratio : $\displaystyle x^2/4$) hence
$\displaystyle \frac{x}{2}\sum_{n=0}^{\infty}\left(\frac{x^2}{4}\ right)^{n}=\frac{x}{2}\cdot \frac{1}{1-\frac{x^2}{4}}=\frac{2x}{4-x^2}\quad \text{\ if\ } \left|\frac{x^2}{4}\right|<1$