Here is one:

[math]\displaystyle 2\sum_{n=1}^{\infty}\sum_{k=1}^{2n}(-1)^{n+1}\frac{(2\pi)^{2n}}{(2n-k+1)!}\left(\frac{1}{2\pi i}\right)^{k} = 1. \tag*{}[/math]

:)