Definition:Geometric Series

Definition

Let $\sequence {x_n}$ be a geometric sequence in $\R$:

$x_n = a r^n$ for $n = 0, 1, 2, \ldots$

Then the series defined as:

$\ds \sum_{n \mathop = 0}^\infty x_n = a + a r + a r^2 + \cdots + a r^n + \cdots$

is a geometric series.