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

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

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    $\begingroup$ You can use Fourier_transformation $\endgroup$
    – Jlamprong
    May 8, 2014 at 12:10
  • $\begingroup$ @Jlamprong Fourier-transformation without complexes??? $\endgroup$
    – peterh
    May 8, 2014 at 12:11
  • $\begingroup$ Yes. see here $\endgroup$
    – Jlamprong
    May 8, 2014 at 12:14
  • $\begingroup$ @Jlamprong Is it me, or complex numbers are clearly mentioned on pages 3, 5, 6, 7 and 8 of the slides you link to? $\endgroup$
    – Did
    May 8, 2014 at 12:41
  • $\begingroup$ I think my answer, while not the shortest, seems to require the fewest prerequisites. Definitely, no complex numbers. $\endgroup$
    – robjohn
    May 29, 2023 at 21:08

2 Answers 2

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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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    $\begingroup$ They are really good proofs. Thanks! $\endgroup$
    – peterh
    May 8, 2014 at 12:42
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I think you have to compute the Fourier series of either $\sin$ or $x$ on $(0,2\pi)$ extended to $\mathbb R$ periodically to get the left hand side and then use Parseval's theorem to prove equivalence to the right hand side.

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