# Chapter 9 - Infinite Series - 9.5 The Comparison, Ratio, And Root Tests - Exercises Set 9.5 - Page 637: 39

Converges

#### Work Step by Step

Factoring out the constant $(\frac{k!}{k^k})$ leaves $$\Sigma^\infty_{k=1} (\frac{k!}{k^k})$$ This is a p-series with p>1. p is greater than 1, so the series Converges

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