Pi Calculation (Ramanujan-Type Formula)

The calculation will end when the current value matches the previous one. Increasing the number of digits used in the calculation will improve the precision of π.

In 1914, the Indian mathematical genius Ramanujan discovered an original formula for calculating pi that converges extremely quickly.
In 1987, the Chudnovsky brothers discovered a Ramanujan-type formula that converges even faster.

Ramanujan-type formula for pi

\(\normalsize\\ (1)\ Ramanujan\ 1,\ 1914\\ \hspace{10px}{\large\frac{1}{\pi}}={\large\frac{\sqrt{8}}{99^2}\displaystyle \sum_{\small n=0}^{\small\infty}\frac{(4n)!}{(4^n n!)^4}\frac{1103+26390n}{99^{4n}}}\\ (2)\ Ramanujan\ 2,\ 1914\\ \hspace{10px}{\large\frac{4}{\pi}}={\large\frac{1}{882}\displaystyle \sum_{\small n=0}^{\small\infty}\frac{(-1)^n(4n)!}{(4^nn!)^4}\frac{1123+21460n}{882^{2n}}}\\ (3)\ Chudonovsky,\ 1987\\ {\large\frac{1}{\pi}}=12{\large\displaystyle \sum_{\small n=0}^{\small\infty}\frac{({\small-}1)^n(6n)!}{(3n)!(n!)^3}\frac{13591409{\small+}545140134n}{(640320^3)^{n+\frac{1}{2}}}}\\ \)