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.



marked as duplicate by Alex, Hakim, Davide Giraudo, Santosh Linkha, JPi May 31 '14 at 12:28

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