College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.3 - Geometric Sequences - 8.3 Exercises: 79

Answer

$\frac{1}{33}$

Work Step by Step

We express the number as a sum of fractions: $0.030303 \ldots=\frac{3}{100}+\frac{3}{10,000}+\frac{3}{1,000,000}+\cdots$ We know that this represents an infinite geometric series with $a=0.03$ and $r= \frac{1}{100}$. We know the sum of an infinite geometric series is: $S_{\infty}=\frac{a}{1-r}$ $S_{\infty}=\frac{0.03}{1-\frac{1}{100}}=\frac{1}{33}$
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