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: 75


Converges to $1$

Work Step by Step

Consider $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} \tan hn $ Since, $\lim\limits_{n \to \infty}e^n=\infty$ So, $\lim\limits_{n \to \infty} \tan hn =\lim\limits_{n \to \infty} \dfrac{e^n-e^{-n}}{e^n+e^{-n}}=\lim\limits_{n \to \infty} \dfrac{1-1/e^{2n}}{1 +1/e^{2n}} $ or, $=1$ Hence, $\lim\limits_{n \to \infty} a_n=1$ and {$a_n$} is convergent and converges to $1$
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