Converge? $\sum_{k=1}^{\infty}\frac{ \sin \left(\frac{1}{k}\right) }{k} $ Determine whether the series converges: 
$$\sum_{k=1}^{\infty}\frac{ \sin \left(\frac{1}{k}\right) }{k} $$
I tired to use direct comparison test but since 1/k is not convergent, so I am not sure about in this case.

Hint
Since you want a direct comparison use this inequality
$$\sin(x)\le x,\; \forall x\ge0$$
