I thought this was the real part of the series: $\sum\_{n=0}^\infty \frac{i^n}{1+2n}$, with $i=\sqrt{-1}$. When taking the real part I am left with: $\sum\_{n=0}^\infty \frac{\cos(n\pi/2)}{1+2n}$. I know this sum is around 0.866973, but I have no idea how to come to this answer. Can someone please help me?