Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 11 - Infinite Sequences and Series - 11.1 Sequences - 11.1 Exercises - Page 744: 42


Converges to $0$

Work Step by Step

Given:$a_n=[ln(n+1)-ln(n)]$ $\lim\limits_{n \to \infty}a_n=\lim\limits_{n \to \infty}[ln(n+1)-ln(n)]$ $=\lim\limits_{n \to \infty}ln[\frac{n+1}{n}]$ $=\lim\limits_{n \to \infty}ln(\frac {n}{n}+\frac{1}{n})$ $=ln(1+0)$ $=ln1$ $=0$ Hence, the sequence converges to $0$.
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