# What is the rationale behind the famous pi formula of Ramanujan [duplicate]

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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, Math1000Sep 18 '16 at 3:58

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• it doesn't look easy, see there and there – reuns Sep 18 '16 at 0:07
• 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. – dxiv Sep 18 '16 at 0:30