prove that :
$\displaystyle \sum_{n=1}^{\infty }(\frac{1}{n^{2}})=\frac{\pi ^{2}}{6}$
Take a peek at this very nice paper: http://www.math.titech.ac.jp/~inoue/...lder/zeta2.pdf
You have there no less than 14 different proofs of the result $\displaystyle \zeta(2)=\sum\limits_{n+1}^{\infty}\frac{1}{n^2}=\ frac{\pi^2}{6}$, from rather basic ones to those that require more knowledge....enjoy!
Tonio