Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 12 - Section 12.3 - Geometric Sequences - 12.3 Exercises - Page 865: 67

Answer

The series is convergent. The sum of the infinite geometric series is $\frac{3}{4}$

Work Step by Step

The series is convergent because |r| $\lt$ 1. r (the common ratio) = -$\frac{1}{3}$ since each term is multiplied by $\frac{1}{3}$ . Use the formula for the sum of an infinite geometric series: S = $\frac{a}{1-r}$ and plug in the first term, 1, for a, and the common ratio, -$\frac{1}{3}$ for r: S = $\frac{1}{1-(-\frac{1}{3})} = \frac{1}{\frac{4}{3}}$ = $\frac{3}{4}$
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