Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 11 - Infinite Series - 11.1 Sequences - Exercises - Page 538: 54


The sequence $a_n$ converges to $0$.

Work Step by Step

We have $$\lim_{n\to \infty}a_n=\lim_{n\to \infty}\frac{n}{2^n}=\frac{\infty}{\infty} .$$ By L'Hopital's rule, we have $$ \lim_{n\to \infty}\frac{n}{2^n}= \lim_{n\to \infty}\frac{1}{2^n\ln 2}=0 .$$ Hence, by Theorem 1, the sequence $a_n$ converges to $0$.
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