(New page: * Infinite geometric series formula assuming <math>|r|<1</math> <math>\sum_{k=1}^\infty ar^{k-1}=\frac{a}{1-r}</math> if <math>|r|<1</math> <math>\sum_{k=1}^\infty kar^{k-1}=\frac{a}{(...) |
(No difference)
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Revision as of 07:07, 23 January 2009
- Infinite geometric series formula assuming $ |r|<1 $
$ \sum_{k=1}^\infty ar^{k-1}=\frac{a}{1-r} $ if $ |r|<1 $
$ \sum_{k=1}^\infty kar^{k-1}=\frac{a}{(1-r)^2} $ if $ |r|<1 $
- Finite sum of a geometric sequence (which does no require $ |r|<1 $)
$ \sum_{k=1}^K ar^{k-1}=\frac{a(1-r^K)}{1-r} $ if $ |r|<1 $
