# Thread: pi summation formula

1. ## pi summation formula

Has anyone seen this one before?.

$\displaystyle \pi=\sum_{n=0}^{\infty}\left(\frac{4}{8n+1}-\frac{2}{8n+4}-\frac{1}{8n+5}-\frac{1}{8n+6}\right)\cdot\left(\frac{1}{16}\right )^{n}$

It works rather well and quick. At n=6 you get 3.14159265357

2. Originally Posted by galactus
Has anyone seen this one before?.

$\displaystyle \pi=\sum_{n=0}^{\infty}\left(\frac{4}{8n+1}-\frac{2}{8n+4}-\frac{1}{8n+5}-\frac{1}{8n+6}\right)\cdot\left(\frac{1}{16}\right )^{n}$

It works rather well and quick. At n=6 you get 3.14159265357
No.

The best one I ever seen was made by Srinivasa Ramanajuan. (search the article for his formula).

3. Originally Posted by galactus
Has anyone seen this one before?.

$\displaystyle \pi=\sum_{n=0}^{\infty}\left(\frac{4}{8n+1}-\frac{2}{8n+4}-\frac{1}{8n+5}-\frac{1}{8n+6}\right)\cdot\left(\frac{1}{16}\right )^{n}$

It works rather well and quick. At n=6 you get 3.14159265357
Never seen that before, but that's nice! I'd love to see how it was derived