Monthly Archives: February 2016

A sum I can only imagine being evaluated using the residue theorem

The challenge this time is to evaluate the following sum: $$\sum_{n=1}^{\infty} \frac{1}{n^3\sin{\left (\sqrt{2} \, n\pi \right)}}$$ NB (20 Nov 2016) I just got word that Wolfram fixed the problem described below. See below for details. It should be clear that the sum converges…right? No? Then how do we show this? Numerical experiments are more or […]