How to see that series $|\sin(1/n^2)|$ converges or diverges? How to see that series $\sum_{n=1}^{\infty}|\sin(1/n^{2})|$ converge or diverge? That is, to see if $\sum_{n}\sin(1/n^{2})$ absolutely converges.
I know that for all $n$ in $\mathbb N$, $\sin(1/n^2)<1/n^2$, but is that fact useful here? Could someone tell me how to show that?

Compare with the convergent series $\sum n^{-2}$, then 
$$ \lim \frac{ \sin (n^{-2}) }{n^{-2}} =_{t = n^{-2}} \lim_{t \to 0} \frac{\sin t }{t} = 1 $$
