How to prove the series $\sum_{n=1}^{\infty} \frac{\sin(\frac{1}n)}n$ converges? $$\sum_{n=1}^{\infty} \frac{\sin(\frac{1}n)}n$$
Using the comparison test/limit comparison test? I have tried the comparison test and several attempts at the limit comparison test, but everything I try points to divergence, which I know isn't true.

The series is convergent:
$$
0\le \frac{\sin\frac 1n}{n} \le \frac{\frac 1n}{n} = \frac 1{n^2} 
$$ and $\sum \frac 1{n^2} <\infty$.
