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: 39


The series is divergent.

Work Step by Step

$a_{n}=arctan(n)$ $\lim\limits_{n \to \infty}a_{n} = \lim\limits_{n \to \infty} arctan(n)$ $=\frac{\pi}{2}$ since [$\lim\limits_{x \to \infty} (tan)^{-1}x = \frac{\pi}{2}$] $\lim\limits_{n \to \infty}a_{n}=\frac{\pi}{2} \ne 0$ So the series is divergent.
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