Prove that $\sum _{n=1}^{\infty }\frac{\sin n}{n}$ converges or diverges.

Asked Sep 23 '20 at 19:28

Active Sep 23 '20 at 19:30

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My guess is that it diverges because 1/n diverges and sin is bounded between [-1,1]; however, I know that the product of two divergent series may yield a convergent. Any suggestions of going about this?

edited Sep 23 '20 at 19:30

K.defaoite

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asked Sep 23 '20 at 19:28

Queen

This and more similar questions can be found with Approach0 – Martin R Sep 23 '20 at 19:32
Wolfram says it converges to $ \frac{1}{2} (\pi - 1) $, but I can't immediately see how it gets there – redroid Sep 23 '20 at 19:36

Prove that $\sum _{n=1}^{\infty }\frac{\sin n}{n}$ converges or diverges.

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