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 1035: 61


$\dfrac {-8}{15}$

Work Step by Step

$\sum ^{\infty }_{i=1}\left( -\dfrac {2}{3}\right) \left( -\dfrac {1}{4}\right) ^{i-1}=\dfrac {a_{1}}{1-r};a_{1}=\left( -\dfrac {2}{3}\right) \times \left( -\dfrac {1}{4}\right) ^{1-1}=-\dfrac {2}{3};r=\left( -\dfrac {1}{4}\right) \Rightarrow S_{\infty }=\dfrac {a_{1}}{1-r}=\dfrac {-\dfrac {2}{3}}{1-\left( -\dfrac {1}{4}\right) }=\dfrac {-8}{15}$
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