Question

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

Answer 1

`oo`

Explanation:

`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`