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: 82

Answer

$\frac{41}{333}$

Work Step by Step

We express the number as a sum of fractions: $0.123123 \ldots=\frac{123}{1000}+\frac{123}{1,000,000}+\frac{123}{1,000,000,000}+...$ We know that this represents an infinite geometric series with $a=\frac{123}{1000}$ and $r= \frac{1}{1000}$. We know the sum of an infinite geometric series is: $S_{\infty}=\frac{a}{1-r}$ $S_{\infty}=\frac{\frac{123}{1000}}{1-\frac{1}{1000}}=\frac{41}{333}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.