Determine whether the series sin^2(1/n) converges or diverges Determine whether the series sin^2(1/n) converges or diverges.
Having real trouble with this one, I know all the terms are positive because it is being squared but I don't know where to begin with showing whether it converges or diverges. From playing with a calculator it seems like the terms are getting smaller so im assuming it converges, any pointers that would help out would be much appreciated.

Is this the sequence or the series?  In fact, both converge.  The sequence obviously converges to $0$. 
The series converges by direct comparison.  Since $|\sin{x}| \leq x$ for all $x > 0$ (prove this!), it follows that $\sum{\sin^2({\frac{1}{n}})} \leq \sum{\frac{1}{n^2}} < \infty$
