# Sum of an infinite series

1. Nov 16, 2011

I was doing my math homework when I started thinking about the sums of two infinite series.
I determined that the sum of the first series $\sum_{n=1}^{\infty} cos(\frac{\pi}{2n})$ diverges. I could not figure out whether or not the series $\sum_{n=1}^{\infty} sin(\frac{\pi}{2n})$ converges or diverges. I think it diverges but I'm unsure because as n approaches infinity each term in the series approaches zero.
Any help would be much appreciated. Thank you in advance

2. Nov 16, 2011

### micromass

Staff Emeritus
Try to do a comparison test. Try to use the inequality:

$$\frac{1}{2}x\leq \sin(x)$$

which holds for small x.