The problem I had was whether this series converges or diverges.

$\displaystyle \sum\limits_{n=10}^n arcsin\frac{\pi}{\sqrt{n}}$

What I did was say that,

$\displaystyle arcsin\frac{\pi}{\sqrt{n}}\geq\frac{1}{\sqrt{n}}$ for every $\displaystyle n$

and since $\displaystyle \sum\limits_{n=10}^n\frac{1}{\sqrt{n}}$ diverges, so must $\displaystyle \sum\limits_{n=10}^narcsin\frac{\pi}{\sqrt{n}} $

The problem here is that, I do not know how to prove that

$\displaystyle arcsin\frac{\pi}{\sqrt{n}}\geq\frac{1}{\sqrt{n}}$

although it seems plausible.