Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 11 - Infinite Sequences and Series - 11.1 Exercises: 65

Answer

a) $a_{1}=1060$ $a_{2}=1123.60$ $a_{3}=1191.02$ $a_{4}=1262.48$ $a_{5}=1338.23$ b) $a_{n}$ is divergent

Work Step by Step

$a_{n}=1000(1.06)^{n}$ a) $a_{1}=1000(1.06)=1060$ $a_{2}=1000(1.06)^{2}=1123.60$ $a_{3}=1000(1.06)^{3}=1191.02$ $a_{4}=1000(1.06)^{4}=1262.48$ $a_{5}=1000(1.06)^{5}=1338.23$ b) $\lim\limits_{n \to \infty}a_{n}=\lim\limits_{n \to \infty}(1000)(1.06)^{n}$ $=1000\lim\limits_{n \to \infty}(1.06)^{n}$ $=\infty$ Thus $a_{n}$ is divergent
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