Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.3 - Geoetric Sequences and Series - Exercise Set - Page 1074: 49



Work Step by Step

The general formula to find the sum of an infinite Geometric series is given as: $ S_{n}=\dfrac{a_1}{(1-r)}$ $0.\overline{257}=\dfrac{257}{1000}+\dfrac{257}{1000000}+\dfrac{257}{1000000000}+......$ Now, $ S_{n}=\dfrac{a_1}{(1-r)}=\dfrac{257/10}{1-\dfrac{1}{1000}}$ Our answer is: $ S_{n}=\dfrac{257/10}{999/1000}=\dfrac{257}{999}$
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