nLab
geometric series

Contents

Definition

The geometric series is the series

n=0 r n. \sum_{n = 0}^\infty r^n \,.

Properties

For rr \in \mathbb{R} with r<1{\Vert r \Vert} \lt 1 this sequence converges

limnk=0nr k=11r. \underset{n \to \infty}{\lim} \underoverset{k = 0}{n}{\sum} r^k \;=\; \frac{1}{1 - r} \,.

References

Last revised on July 18, 2017 at 14:16:06. See the history of this page for a list of all contributions to it.