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: 80

Answer

$\frac{10457}{4950}$

Work Step by Step

We express the number as a sum of fractions: $2.112525.. =2.11+ \frac{25}{10,000}+\frac{25}{1,000,000}+\frac{25}{100,000,000}+...$ We know that this represents an infinite geometric series with $a=\frac{25}{10000}$ and $r= \frac{1}{100}$ (added to $2.11$). We know the sum of an infinite geometric series is: $S_{\infty}=\frac{a}{1-r}$ $S_{\infty}=\frac{\frac{25}{10000}}{1-\frac{1}{100}}=\frac{25}{9900}$ We add this to $2.11$: $2.11+\frac{25}{9900}=\frac{211}{100}+\frac{25}{9900}=\frac{211*99+25}{9900}=\frac{20914}{9900}=\frac{10457}{4950}$
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