Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 11 - Section 11.1 - Sequences - 11.1 Exercises: 42

Answer

The sequence converges to $\ln{1} = 0$.

Work Step by Step

Write $\ln{(n+1)} - \ln{n}$ as $\ln{(\frac{n+1}{n})} = \ln{(1 + \frac{1}{n})}$. By continuity of limits, we can take the limit inside the natural log. Since the limit of $1 + \frac{1}{n}$ is 1, we see that our sequence converges to $\ln{1} = 0$.
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