Does the series [math]\displaystyle \sum_{n=1}^\infty(-1)^n\tan\left(\frac{\pi}{n+2}\right)\sin\left(\frac{n\pi}{3}\right)[/math] converge and why?
Does the series [math]\sum_{i = 1}^ \infty \frac{(-1)^n}{(n-1)!  -  1}[/math] converge?