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

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?

• Your title and question body are different? – Zain Patel Apr 18 '18 at 20:00
• 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? – Mark Viola Apr 18 '18 at 20:01
• 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. – DonAntonio Apr 18 '18 at 20:04
• Why the title is different? I'm going to change it. – user Apr 18 '18 at 20:10
• @DonAntonio Clearly the OP is about the solved one, I've changed the title. – user Apr 18 '18 at 20:13

$$\left|\frac{\sin n}{n!}\right|\le\frac1{n!}$$
• and $\frac1{n!}$ seems to be very prone to converge :) – user Apr 18 '18 at 20:09