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This question already has an answer here:

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:


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

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

up vote 5 down vote accepted

An idea:

$$\sin^2n=\frac12(1-\cos 2n)$$

Now, using Dirichlet's test we get that


and since the harmonic series diverges then our series diverges as well.

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