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: 19

Answer

$S_{\infty}=\dfrac{16}{9}$

Work Step by Step

Using $S_{\infty}=\dfrac{a_1}{1-r}$, the sum of the infinite geometric sequence $ 2,-\dfrac{1}{4},\dfrac{1}{32},... $ is \begin{array}{l} S_{\infty}=\dfrac{2}{1-\left( -\dfrac{1}{8} \right)}\\\\ S_{\infty}=\dfrac{2}{\dfrac{9}{8}}\\\\ S_{\infty}=\dfrac{16}{9} .\end{array}
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