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I need to prove the convergence of: $\sum_{n=1}^\infty\frac{\sin(n)}{n}$.

To do it I wanted to use the alternating series test. I know that $a_n=1/n\overset{n\rightarrow \infty }{\rightarrow} 0$ but for example $\sin(1)>0$ and $\sin(2)>0$ so I can't use it directly. What should I do?

Aaron Hendrickson
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    https://math.stackexchange.com/q/4073653/42969, https://math.stackexchange.com/q/4084055/42969, https://math.stackexchange.com/q/2227574/42969 – these (and more) can be found with Approach0 – Martin R May 24 '22 at 11:19
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    Welcome to the Math Stack Exchange. For future questions please be courteous and spell check your questions before posting to the site. Thank you. – Aaron Hendrickson May 24 '22 at 11:19
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    The alternating series test is a special case of Dirichlet's test. Try using Dirichlet's test instead. – Gary May 24 '22 at 11:20
  • Thank you for your help –  May 24 '22 at 11:29
  • See also my answer here https://math.stackexchange.com/a/4084102/399263 where I show a way to prove it directly (well in fact it is kind of the Dirichlet test, but with a shortcut for this particular case). – zwim May 24 '22 at 12:09

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