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Every times I look at this formula I get astonished: $$\frac{1}{\pi} = \frac{2 \sqrt 2}{99^2} \sum_{k=0}^\infty \frac{(4k)!}{k!^4} \frac{26390k+1103}{396^{4k}}.$$

Can someone give me an idea of the reasoning behind that formula?


marked as duplicate by Sri-Amirthan Theivendran, Joel Reyes Noche, Shailesh, user223391, Math1000 Sep 18 '16 at 3:58

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    $\begingroup$ it doesn't look easy, see there and there $\endgroup$ – reuns Sep 18 '16 at 0:07
  • $\begingroup$ There are proofs of that formula, as linked above and elsewhere. But as far as I know Ramanujan never gave a hint of how he found it himself. $\endgroup$ – dxiv Sep 18 '16 at 0:30

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