Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 11 - Section 11.4 - Partial Sums of Arithmetic and Geometric Sequences - Exercise Set - Page 658: 21

Answer

$S_{\infty}=\dfrac{4}{9}$

Work Step by Step

Using $S_{\infty}=\dfrac{a_1}{1-r}$, the sum of the infinite geometric sequence $ \dfrac{2}{3},-\dfrac{1}{3},\dfrac{1}{6},... $ is \begin{array}{l} S_{\infty}=\dfrac{\dfrac{2}{3}}{1-\left( -\dfrac{1}{2} \right)}\\\\ S_{\infty}=\dfrac{\dfrac{2}{3}}{\dfrac{3}{2}}\\\\ S_{\infty}=\dfrac{4}{9} .\end{array}
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