Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 11 - Further Topics in Algebra - 11.3 Geometric Sequences and Series - 11.3 Exercises - Page 1034: 45

Answer

$$\left| r \right| < 1$$

Work Step by Step

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