| Power Series Formulas | |
|---|---|
| Taylor Series | |
| exponential | $ e^x = \sum_{n=0}^\infty \frac{x^n}{n!}, $ for all $ x\in {\mathbb C}\ $ |
| Geometric Series | |
| Finite Geometric Series Formula | $ \sum_{k=0}^n x^k = \left\{ \begin{array}{ll} \frac{1-x^{n+1}}{1-x}&, \text{ if } x\neq 1\\ n+1 &, \text{ else}\end{array}\right. $ |
| Infinite Geometric Series Formula | $ \sum_{k=0}^n x^k = \left\{ \begin{array}{ll} \frac{1}{1-x}&, \text{ if } |x|\leq 1\\ \text{diverges} &, \text{ else }\end{array}\right. $ |
| Other Series | |
| notes/name | equation |
