Geometric Series

analysis

Definition

Geometric Series

A series of form:

$$\sum _{n\ge 0}{q}^n=1+q+q^2+q^3+\dots$$

is called geometric series.

Divergence

For $|q|\ge 1$, the geometric series is divergent, since the sequence of terms, i.e., $(q^n{)}_{n\in \mathbb{N}}$ is not a null sequence.