(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}{(...) |
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− | + | [[Category:ECE302Spring2009chihw]] | |
− | + | == Infinite geometric series formula assuming <math>|r|<1</math> == | |
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− | * | + | * <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> | |
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+ | == Finite sum of a geometric sequence (which does no require <math>|r|<1</math>) == | ||
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+ | * <math>\sum_{k=1}^K ar^{k-1}=\frac{a(1-r^K)}{1-r}</math> |
Latest revision as of 05:45, 26 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} $