The following formula for π was discovered by Ramanujan:

1π=2√29801∞∑k=0(4k)!(1103+26390k)(k!)43964kDoes anyone know how it works, or what the motivation for it is?

**Answer**

Here’s an easy introduction to the basics, “*Pi Formulas and the Monster Group*“.

http://sites.google.com/site/tpiezas/0013

**Update:** Just to make this more intriguing, define the *fundamental unit* U29=5+√292 and fundamental solutions to *Pell equations*,

(U29)3=70+13√29,thus702−29⋅132=−1

(U29)6=9801+1820√29,thus98012−29⋅18202=1

26((U29)6+(U29)−6)2=3964

then we can see those integers all over the formula as,

1π=2√29801∞∑k=0(4k)!k!429⋅70⋅13k+1103(3964)k

See also this MO post.

**Attribution***Source : Link , Question Author : Nick Alger , Answer Author : Community*