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 - Page 704: 54

Answer

Converges to $0$

Work Step by Step

We can divide the sequence into two sub-sequences, namely, the odd-numbered terms ($\frac{1}{n}$) as $\frac{1}{1},\frac{1}{2},\frac{1}{3},\frac{1}{4},...$ and the even-numbered terms ($\frac{1}{n+2}$) as $\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6},...$ the other sub-sequence. We can see that the limit of both sub-sequences is $0$ as $n \to \infty $ ; therefore, the limit of the sequence is $0$ as well. Hence, the given sequence converges to $0$.
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