## Zeta (2) Function

1. The problem statement, all variables and given/known data

Find the shortest way possible to prove:

2. Relevant equations

$$\zeta (2)=\frac{\pi^{2}}{6}$$

3. The attempt at a solution

I trying doing sinx < x < tanx if u know what I mean but it took me 6 pages.
I want a prove that is short and concise.
Also, can you guys please show full working?
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 Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus Is this really homework? May I know what your mathematical background is?? I ask this because the shortest possible proofs will require quite some mathematical knowledge such as Fourier series or complex analysis.

 Quote by micromass Is this really homework? May I know what your mathematical background is?? I ask this because the shortest possible proofs will require quite some mathematical knowledge such as Fourier series or complex analysis.
Yes, I just want the shortest possible prove, a really concise prove.
Show me the prove, and leave the rest for me, I'll understand it.