TITLE: Showing $\sum _{k=1} 1/k^2 = \pi^2/6$
QUESTION [6 upvotes]: Possible Duplicate:
Different methods to compute $\sum\limits_{n=1}^\infty \frac{1}{n^2}$
Does $\sum\limits_{k=1}^n 1 / k ^ 2$ converge when $n\rightarrow\infty$? 

I read my book of EDP, and there appears the next serie
$$\sum _{k=1} \dfrac{1}{k^2} = \dfrac{\pi^2}{6}$$
And, also, we prove that this series is equal $\frac{\pi^2}{6}$ for methods od analysis of Fourier, but...
Do you know other proof, any more simple or beautiful?

REPLY [15 votes]: Fourteen proofs compiled by Robin Chapman.
http://empslocal.ex.ac.uk/people/staff/rjchapma/etc/zeta2.pdf