Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 10: Infinite Sequences and Series - Section 10.2 - Infinite Series - Exercises 10.2 - Page 580: 38

Answer

Diverges; Limit does not exist

Work Step by Step

The nth partial sums are: $ s_n=(\tan 1-\tan 0)+(\tan 2-\tan 1)+...(\tan {n+1} -\tan n)=\tan (n+1)$ Since, the value for $\tan x$ is always oscillates in between $-\infty$ and $+\infty$. Then after applying limits , we have $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} \tan (n+1)$ This implies that Limit does not exist Now, the given series diverges.
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