I have to determine the following sum:
\begin{equation} \sum\limits_{n=0}^{\infty}\frac{(-1)^n}{2n+1} \end{equation}
And i've tried lot's of ways to determine it, but i couldn't get a result so I figured I would look on WolframAlpha to see what the result has to be so i could maybe know what to do next by that. But apparently the result is $\frac{\pi}{4}$ and i don't know how I could possibly get to pi. Does anyone have any suggestions about how to tackle this?