Answer
Diverges
Work Step by Step
Factoring out the constant $\frac{k!}{k^3}$ leaves
$$\Sigma^m_{k=1} \frac{k!}{k^3}$$
This is a p-series with p<1, so the series diverges.
Calculus, 10th Edition (Anton)
by Anton, Howard
Published by
Wiley
ISBN 10:
0-47064-772-8
ISBN 13:
978-0-47064-772-1
Chapter 9 - Infinite Series - 9.5 The Comparison, Ratio, And Root Tests - Exercises Set 9.5 - Page 636: 15
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