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: 50


Converges to $1$

Work Step by Step

Consider $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} \dfrac{\ln n}{\ln 2n}$ But $\lim\limits_{n \to \infty} \dfrac{\ln n}{\ln 2n}=\dfrac{\infty}{\infty}$ Need to apply L-Hospital's rule. So, $\lim\limits_{n \to \infty} \dfrac{\ln n}{\ln 2n}=\lim\limits_{n \to \infty} \dfrac{1/n}{2/2n}$ or, $=1$ Hence, $\lim\limits_{n \to \infty} a_n=1 $ and {$a_n$} is convergent and converges to $1$.
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