A Ramanujan Series

In this article we prove the following Ramanujan series


\begin{align*} & \sum_{n=1}^{\infty} \frac{(-1)^{n}}{n^3 \sinh n \pi}=-\frac{\pi^3}{360} \\ & \sum_{n=1}^{\infty} \frac{(-1)^{n}}{n^7 \sinh n \pi}=-\frac{13 \pi^7}{453600} \\ & \sum_{n=1}^{\infty} \frac{(-1)^{n}}{n^{11} \sinh n \pi}=-\frac{4009 \pi^{11}}{13621608000} \end{align*}



To this end we will rely on the residues theorem. 

Click here  for the proof of the Ramanujan´s series

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