University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 9 - Section 9.1 - Sequences - Exercises - Page 488: 43


$\lim\limits_{n \to \infty} a_n=1$ and {$a_n$} is convergent.

Work Step by Step

Consider $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} \sin (\dfrac{\pi}{2}+\dfrac{1}{n})$ $\lim\limits_{n \to \infty} \sin (\dfrac{\pi}{2}+\dfrac{1}{n})=\sin (\lim\limits_{n \to \infty}\dfrac{\pi}{2}+\lim\limits_{n \to \infty}\dfrac{1}{n})$ or, $=\sin \dfrac{\pi}{2}$ or, $=1$ Thus, $\lim\limits_{n \to \infty} a_n=1$ and {$a_n$} is convergent.
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