I am trying to determine whether the
$$ \sum_{n=1}^{\infty} \left(\frac{\sin(n)}{n}\left ( \sum_{m=1}^{n}\frac{1}{m} \right ) \right) $$
converges or not. I have tried the popular tests, but all were inconclusive (so perhaps I am doing it wrong...).
I would appreciate any help and explanation on how I should solve it.
Thanks.