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: 38


The series is convergent with a sum $\frac{cos1}{1-cos1}$.

Work Step by Step

$\Sigma^{\infty}_{k=1} (cos 1)^{k} = \Sigma^{\infty}_{k=1} (cos 1)(cos 1)^{k-1}$ It is a geometric series with $r=cos1$ and $a=cos1$ Since $|r|=|cos1| \lt 1$, the series is convergent and has a sum $\Sigma^{\infty}_{k=1} (cos 1)^{k} = \frac{a}{1-r}$ $= \frac{cos1}{1-cos1}$ $\approx 1.175343$
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