Leibniz's Formula for Pi

Theorem

 * $\displaystyle \frac \pi 4 = 1 - \frac 1 3 + \frac 1 5 - \frac 1 7 + \frac 1 9 - \cdots $

That is:
 * $\displaystyle \pi = 4 \sum_{k \mathop \ge 0} \left({-1}\right)^k \frac 1 {2 k + 1}$

Also known as
Leibniz's Formula for Pi is also known as the Gregory Series for James Gregory.