Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 11 - Infinite Sequences and Series - 11.2 Exercises - Page 735: 19



Work Step by Step

The values in the sequence are getting smaller and smaller in a geometric sequence. When we divide consecutive terms, we see we have a common ratio of -1/5. We can use the formula $S_{y}=a/(1-r)$, where a is the first term and r is the ratio between terms. When we plug in $a=10$ and $r=-1/5$, we get: $S_{y}=10/(1--1/5)=10/(6/5)=50/6=25/3$
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