College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 8 - Sequences, Induction, and Probability - Exercise Set 8.3 - Page 742: 87

Answer

$\frac{1}{3}$

Work Step by Step

The total area can be represented by the sum of the infinite geometric series with first term $a_1=0.25$ and common ratio $r=0.25$. An infinite geometric series converges if and only if $|r|\lt1$, where $r$ is the common ratio. If it converges, then it equals $\frac{a_1}{1-r}$ where $a_1$ is the first term. Here $0.25\lt1$. Hence the sum: $\dfrac{0.25}{1-0.25}=\frac{1}{3}$
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