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 - 11.2 Exercises - Page 735: 10

Answer

The series is divergent. See graph
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Work Step by Step

$a_{n}=\Sigma^{\infty}_{n=1}cosn$ partial sum: $s_{n}=a_{1} + a_{2}+... +a_{n}$ $n=1$ $s_{1}=0.5403$ $a_{1}=0.5403$ $n=2$ $s_{2}=0.1242$ $a_{2}=-0.4161$ $n=3$ $s_{3}=-0.8658$ $a_{3}=-0.9900$ $n=4$ $s_{4}=-1.5195$ $a_{4}=-0.6536$ $n=5$ $s_{5}=-1.2358$ $a_{5}=0.2837$ $n=6$ $s_{6}= -0.2756$ $a_{6}=0.9602$ $n=7$ $s_{7}=0.4783$ $a_{7}=0.7539$ $n=8$ $s_{8}=0.3328$ $a_{8}=-0.1455$ $n=9$ $s_{9}=-0.5784$ $a_{9} =-0.9111$ $n=10$ $s_{10}=-1.4174$ $a_{10}=-0.8391$ The series appears to be divergent because it oscillates from negative to positive forever.
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