Definition:Geometric Series

Definition
Let $\left \langle{x_n}\right \rangle$ be a geometric progression in $\R$:


 * $x_n = a r^{n-1}$ for $n = 1, 2, 3, \ldots$

Then the series defined as:
 * $\displaystyle \sum_{n \mathop = 1}^\infty x_n = a + ar + ar^2 + \cdots + ar^n + \cdots$

is a geometric series.