We want to determine if the sequence \frac{n^{n}}{n!} is monotonic.

Using the ratio test we get that\frac{s_{n+1}}{s_{n}} = \bigl(
\bigr) ^ n
<
=
>
\hskip 5pt 1

Hence the sequence is
monotone decreasing
monotone increasing
monotone nonincreasing
monotone nondecreasing
cannot be determined

Using the ratio test we get that

Hence the sequence is

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