Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 10: Infinite Sequences and Series - Section 10.2 - Infinite Series - Exercises 10.2 - Page 580: 59



Work Step by Step

Formula to calculate the sum of a geometric series is: $S=\dfrac{a}{1-r}$; Since, we have two series $\sum_{n =0}^{ \infty} (\dfrac{2}{3})^n$ and $\sum_{n =0}^{ \infty} (\dfrac{1}{3})^n$ Both series are a convergent geometric series with first term, $a=1$ and common ratio $r =\dfrac{2}{3}, \dfrac{1}{3}$ Thus, $S=\dfrac{1}{1-\dfrac{2}{3}}-\dfrac{1}{1-\dfrac{1}{3}}$ or, $=\dfrac{3}{3-1}$ or, $=\dfrac{3}{2}$
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