Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 11 - Infinite Sequences and Series - Review - Exercises - Page 825: 29



Work Step by Step

$$\Sigma_{n=1}^{\infty}[tan^{-1}(n+1)-tan^{-1}n]=\lim\limits_{k \to \infty}\Sigma_{n=1}^{k}[tan^{-1}(n+1)-tan^{-1}n]$$$$=\lim\limits_{k \to \infty}tan^{-1}(k+1)-tan^{-1}1$$$$=\frac{\pi}{2}-\frac{\pi}{4}$$$$=\frac{\pi}{4}$$
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