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| − | * <math>\sum_{k=1}^\infty ar^{k-1}=\frac{a}{1-r} | + | * <math>\sum_{k=1}^\infty ar^{k-1}=\frac{a}{1-r}</math> |
| − | * <math>\sum_{k=1}^\infty kar^{k-1}=\frac{a}{(1-r)^2} | + | * <math>\sum_{k=1}^\infty kar^{k-1}=\frac{a}{(1-r)^2}</math> |
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| − | * <math>\sum_{k=1}^K ar^{k-1}=\frac{a(1-r^K)}{1-r} | + | * <math>\sum_{k=1}^K ar^{k-1}=\frac{a(1-r^K)}{1-r}</math> |
Revision as of 07:10, 23 January 2009
Infinite geometric series formula assuming $ |r|<1 $
- $ \sum_{k=1}^\infty ar^{k-1}=\frac{a}{1-r} $
- $ \sum_{k=1}^\infty kar^{k-1}=\frac{a}{(1-r)^2} $
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} $
