Pi - Ramanujan's Formula for Pi

Ramanujan's Formula for Pi

First found by Ramanujan. It's my favourite formula for pi. I have no idea how it works.

\frac{1}{π} = \frac{\sqrt{8}}{9801} \sum_{n = 0}^{∞} \frac{(4 n)!}{(n!)^{4}} \times \frac{26390 n + 1103}{396^{4 n}}

A Ramanujan-type formula due to the Chudnovsky brothers used to break a world record for computing the most digits of pi:

\frac{1}{π} = \frac{1}{53360 \sqrt{640320}} \sum_{n = 0}^{∞} (- 1)^{n} \frac{(6 n)!}{n!^{3} (3 n)!} \times \frac{13591409 + 545140134 n}{640320^{3 n}}

For implementations, it may help to use $640320^{3} = 8 \cdot 100100025 \cdot 327843840$