\( \newcommand{\cat}[1] {\mathrm{#1}} \newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})} \newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}} \)

Geometric series

Let \( x \) be a real number. If \( |x| \ge 1 \), then the series \( \sum_{n=0}^{\infty} x^n \) is divergent. If however \( |x| \le 1 \), then the series is absolutely convergent and the sum is given by:

On the reverse side, there is some geometric visual reasoning; can you remember what it looks like?