Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 11 - Section 11.2 - Series - 11.2 Exercises - Page 748: 50

Answer

Divergent

Work Step by Step

$a_{n}=\frac{e^{n}}{n^{2}}$ $\lim\limits_{n \to \infty} a_{n} = \lim\limits_{n \to \infty}\frac{e^{n}}{n^{2}}$ Use L'hospital's rule $=\lim\limits_{n \to \infty} \frac{e^{n}}{2n}$ $=\lim\limits_{n \to \infty} \frac{e^{n}}{2}$ $=\infty$ $\ne 0$ Therefore the series is divergent.
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