University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 9 - Section 9.1 - Sequences - Exercises - Page 488: 81

Answer

Converges to $\dfrac{\pi}{2}$

Work Step by Step

Consider $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} tan^{-1} n$ Since, $ \lim\limits_{n \to \dfrac{\pi}{2}} \tan x=\dfrac{\pi}{2}$ So, $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} tan^{-1} n=\dfrac{\pi}{2}$ Hence, $\lim\limits_{n \to \infty} a_n=\dfrac{\pi}{2}$ and {$a_n$} is Convergent and converges to $\dfrac{\pi}{2}$
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