How do you determine the limit of $n^n/(n!)$ as n approaches infinity?

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Answer 1 · 2016-07-11T13:32:43

$oo$

$n^n/(n!)=prod_{k=1}^n (n/k) = prod_{k=1}^{n-1}(n/k)$

but here each $n/k > 1$

then $lim_{n->oo}prod _{k=1}^{n-1}(n/k) = oo$

How do you determine the limit of n^n/(n!)n^n/(n!) as n approaches infinity?