> 
> Does the serie $\displaystyle\sum\_{n=1}^{\infty}\Bigl(1-\cos\frac{\pi}{n}\Bigr)$ converge?
> 
> 
> 

Limit test of $1-\cos\frac{\pi}{n}$

$$
\lim\_{x\to\infty} 1-\cos\frac{\pi}{n} =
1 -\lim\_{n\to\infty}\cos\frac{\pi}{n}= 1-1 = 0
$$

I've checked the necessary condition that $\lim\_{n\to\infty} 1-\cos\frac{\pi}{n} = 0 $

But how do I check if $\sum\_{n=1}^{\infty}(1-\cos\frac{\pi}{n})$ converges?