- #1

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## Homework Statement

[tex]\Sigma[/tex]n!/n^n

index n=1 to infinity

## Homework Equations

## The Attempt at a Solution

Using the Ratio test (limit as n goes to infinity of a[tex]_{n+1}[/tex]/a[tex]_{n}[/tex])

and found that the series converges.

However, I thought that factorials grew faster than exponential functions. Therefore, it would diverge, right?

Could someone explain why? Did I just do something wrong?