Answer
$$\left| r \right| < 1$$
Work Step by Step
$$\eqalign{
& {\text{The sum }}{S_\infty }{\text{ of the terms of an infinite geometric sequence with }} \cr
& {\text{first term }}{a_1}{\text{ and common ratio }}r,{\text{ where }}\left| r \right| < 1,{\text{ is given by the }} \cr
& {\text{following:}} \cr
& {S_\infty } = \frac{{{a_1}}}{{1 - r}} \cr
& {\text{Then the sum exists if }}\left| r \right| < 1. \cr} $$