# Pi (Ramanujan's formula) Calculator

## Calculates circular constant Pi using the Ramanujan-type formula.

 formula Ramanujan 1 1914 Ramanujan 2 1914 Chudonovsky 1987
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 The calculation ends when two consecutive results are the same.The accuracy of π improves by increasing the number of digits for calculation.In 1914, the Indian mathematician Ramanujan discovered the formula for computing Pi that converges rapidly. In 1987, Chudnovsky brothers discovered the Ramanujan-type formula that converges more rapidly.Ramanujan's formula for Pi$\normal\\\vspace{5}(1)\ Ramanujan\ 1,\ 1914\\\hspace{10}{\large\frac{1}{\pi}}={\large\frac{\sqrt{8}}{99^2}\sum_{\small n=0}^{\small\infty}\frac{(4n)!}{(4^n n!)^4}\frac{1103+26390n}{99^{4n}}}\\\vspace{5}(2)\ Ramanujan\ 2,\ 1914\\\hspace{10}{\large\frac{4}{\pi}}={\large\frac{1}{882}\sum_{\small n=0}^{\small\infty}\frac{(-1)^n(4n)!}{(4^nn!)^4}\frac{1123+21460n}{882^{2n}}}\\\vspace{5}(3)\ Chudonovsky,\ 1987\\{\large\frac{1}{\pi}}=12{\large\sum_{\small n=0}^{\small\infty}\frac{({\small-}1)^n(6n)!}{(3n)!(n!)^3}\frac{13591409{\small+}545140134n}{(640320^3)^{n+\frac{1}{2}}}}\\$

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