Solving an exercise today I came across this series and I'm curious to know if we can evaluate it. Here it is:
$$\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}} \arctan \frac{1}{n \sqrt{n}}$$
It rings me bells about some other series with arctan's I have come across but I could not see any similarity on how to begin. Wolfram gives an approximation of $1.41379$. Note that $\sqrt{2} \approx 1.4142$. Too sad !!