University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 9 - Section 9.1 - Sequences - Exercises - Page 487: 6

Answer

$a_1=\frac{1}{2}$ $a_2=\frac{3}{4}$ $a_3=\frac{7}{8}$ $a_4=\frac{15}{16}$

Work Step by Step

We know that $a_n=\frac{2^n-1}{2^n}$. Hence, here: $a_1=\frac{2^1-1}{2^1}=\frac{2-1}{2}=\frac{1}{2}$ $a_2=\frac{2^2-1}{2^2}=\frac{4-1}{4}=\frac{3}{4}$ $a_3=\frac{2^3-1}{2^3}=\frac{8-1}{8}=\frac{7}{8}$ $a_4=\frac{2^4-1}{2^4}=\frac{16-1}{16}=\frac{15}{16}$
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