Ramanujan's famous pi formula states that \begin{equation} \frac{1}{\pi}=\frac{2\sqrt{2}}{99^2}\sum_{k=0}^{\infty}\frac{(4k)!}{k!^4}\frac{26390k+1103}{396^{4k}} \end{equation} How can one prove this? If the proof is too long for this site, you can reference any article containing the proof.

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Ramanujan's Series for 1/π: A Surveydoi.org/10.1080/00029890.2009.11920975 (pdf), which references J. M. Borwein and P. B. Borwein,Pi and the AGM; A Study in Analytic Number Theory and Computational Complexity, Wiley, New York, 1987 (publisher page. as containing the first proofs. $\endgroup$ – David Roberts Oct 10 at 7:19