Monday, August 28, 2017

real analysis - Proof for $sum_{n=1}^{infty}frac{1}{n^2}=frac{pi^2}{6}$ without complexes?





This is what I needed. Practically, a link were also okay.



$$\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}$$


Answer



Evaluating ζ(2) by Robin Chapman contains several proofs (~14 altogether). You can have a look through and find a nice one.


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