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: 38

Answer

The sequence converges to $1$.

Work Step by Step

We can write $\ln{2n}$ as $\ln{2} + \ln{n}$. Hence $$a_n = \frac{\ln{n}}{\ln{2} + \ln{n}} = \frac{1}{\frac{\ln{2}}{\ln{n}} + 1}.$$ Since the fraction in the denominator approaches 0 as $n \to \infty$, our sequence converges to $\frac{1}{0 + 1} = 1$.
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