[Math] How to show that $\sum_{n=1}^{\infty} (-1)^n \sin(\pi/n)$ converges

Question

I'm a bit lost because I know that the alternating series test doesn't apply here. I've shown that it does not converge absolutely using the limit comparison test, but right now the only way I know this series actually converges is by typing it into Wolfram Alpha.

Answer 1

After you remove the $n=1$ case, what can you say about $\sin(\pi/n)$?