# hard time with series convergence or divergence [duplicate]

I'm having real hard time with this series

I can't prove that the series converges and also I can't prove that the series diverges:

$$\sum_{k=1}^\infty\frac{\sin^2(n)}{n}.$$

any help would be appreciated.

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## marked as duplicate by David Mitra, Henry T. Horton, Amzoti, Martin, draks ...Jun 19 '13 at 20:41

$$\sin^2n=\frac12(1-\cos 2n)$$
$$\sum_{n=1}^\infty\frac{\cos2n}n\;\;\text{converges}$$