Chip and Josh in class today gave the series $\sum_{i=1}^{k} (-1)^{i-1}\frac{4} {2 i - 1} = 4 - \frac{4}{3} + \frac{4}{5} - \frac{4}{7} ...$ as an example of a series that converges to $\pi$.

After doing some further research, I stumbled upon two other series that have convergence related to $\pi$:

**Ramanujan's Formula**

**Chudnovsky Algorithm**

The Chudnovsky Algorithm is based on a rapidly converging hypergeometric series. It was used to generate over a billion digits of $\pi$! Mathematica uses it today to calculate $\pi$.