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Different methods to compute $\sum\limits_{n=1}^\infty \frac{1}{n^2}$

What is the simplest way to show $$\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}$$ using only power series but not Fourier series?

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Z.H.
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    Do any of the methods mentioned at http://math.stackexchange.com/questions/8337/different-methods-to-compute-sum-limits-n-1-infty-frac1n2 answer your question? It is not clear to me what "using only power series" means. – Qiaochu Yuan May 25 '12 at 01:54
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    Different proofs can be found here(http://math.stackexchange.com/questions/8337/different-methods-to-compute-sum-limits-n-1-infty-frac1n2) and here(http://empslocal.ex.ac.uk/people/staff/rjchapma/etc/zeta2.pdf). –  May 25 '12 at 01:57
  • Thanks. I didn't know how to search for questions with math formulas. – Z.H. May 25 '12 at 02:09

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