# Chapter 8 - Sequences and Infinite Series - 8.4 The Divergence and Integral Tests - 8.4 Exercises - Page 638: 18

Inconclusive

#### Work Step by Step

$\lim _{n\rightarrow \infty }\dfrac {k^{3}}{k!}=\lim _{k\rightarrow \infty }\dfrac {k\times k\times k}{1\times 2\times \ldots \times \left( k-1\right) \times k}=\lim _{k\rightarrow \infty }\dfrac {k\times k}{1\times 2\times \ldots \times \left( k-2\right) \left( k-1\right) }=\lim _{k\rightarrow \infty }\dfrac {1}{1\times 2\times \ldots \times \left( 1-\dfrac {2}{k}\right) \left( 1-\dfrac {1}{k}\right) }=0$ Then test is inconclusive.

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