Does $\sum\frac{\sin n}{n!}$ converge?

Because of n! I thought of the ratio test, but the sin(n) would be a problem. Any tips?

  • $\begingroup$ Your title and question body are different? $\endgroup$ – Zain Patel Apr 18 '18 at 20:00
  • $\begingroup$ The denominator in the title is $n$ while it is $n!$ in the main body of the question. Which is the one of interest here? $\endgroup$ – Mark Viola Apr 18 '18 at 20:01
  • $\begingroup$ I rolled back to the original question to make clearer the OP has two different series in the title and in the body of the question. $\endgroup$ – DonAntonio Apr 18 '18 at 20:04
  • $\begingroup$ Why the title is different? I'm going to change it. $\endgroup$ – user Apr 18 '18 at 20:10
  • $\begingroup$ @DonAntonio Clearly the OP is about the solved one, I've changed the title. $\endgroup$ – user Apr 18 '18 at 20:13


$$\left|\frac{\sin n}{n!}\right|\le\frac1{n!}$$

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  • 1
    $\begingroup$ and $\frac1{n!}$ seems to be very prone to converge :) $\endgroup$ – user Apr 18 '18 at 20:09

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