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 $
