Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 10: Infinite Sequences and Series - Section 10.1 - Sequences - Exercises 10.1 - Page 569: 7


$a_1$=$1$ $a_2$=$\frac{3}{2}$ $a_3$=$\frac{7}{4}$ $a_4$=$\frac{15}{8}$ $a_5$=$\frac{31}{16}$ $a_6$=$\frac{63}{32}$ $a_7$=$\frac{127}{64}$ $a_8$=$\frac{255}{128}$ $a_9$=$\frac{511}{256}$ $a_{10}$=$\frac{1023}{512}$

Work Step by Step

$a_1$=$1$ $a_2$=$1+\frac{1}{2}$=$\frac{3}{2}$ $a_3$=$\frac{3}{2}+\frac{1}{(2)^2}$=$\frac{7}{4}$ $a_4$=$\frac{7}{4}+\frac{1}{(2)^3}$=$\frac{15}{8}$ $a_5$=$\frac{15}{8}+\frac{1}{(2)^4}$=$\frac{31}{16}$ $a_6$=$\frac{63}{32}$ $a_7$=$\frac{127}{64}$ $a_8$=$\frac{255}{128}$ $a_9$=$\frac{511}{256}$ $a_{10}$=$\frac{1023}{512}$
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