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! colspan="2" style="background: #e4bc7e; font-size: 110%;" | Power Series Formulas | ! colspan="2" style="background: #e4bc7e; font-size: 110%;" | Power Series Formulas | ||
| + | |- | ||
| + | ! colspan="2" style="background: #eee;" | Taylor Series | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | exponential || <math>e^x = \sum_{n=0}^\infty \frac{x^n}{n!},</math> for all <math> x\in {\mathbb C}\ </math> | ||
|- | |- | ||
! colspan="2" style="background: #eee;" | Geometric Series | ! colspan="2" style="background: #eee;" | Geometric Series | ||
Revision as of 07:35, 30 October 2009
| 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 |
