Answer
No.
Work Step by Step
No, the student is wrong. The alternating series has the form $\sum_{n=1}^{\infty}(-1)^{n-1} b_{n}$, where $b_n$ is decreasing and $\lim_{n\to \infty}$, and $\sqrt n$ does not satisfy any of these properties.
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 11 - Infinite Series - 11.4 Absolute and Conditional Convergence - Preliminary Questions - Page 562: 3
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