Leibniz's Formula for Pi

Theorem

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

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