Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 11 - Infinite Sequences and Series - 11.1 Exercises: 31

Answer

Diverges.

Work Step by Step

Since the highest degree of $n$ in the numerator is 2 and the highest degree in the denominator is 3/2, the limit as $n$ approaches infinity will be that of $\frac{n^2}{n^{3/2}} = \sqrt{n}$. Hence the sequence diverges.
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