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`sum_(n=1)^oo (n!)/n^n` Use the Root Test to determine the convergence or divergence of the series.

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The Root Test says that this limit will converge if and only if the following limit (actually limit superior) is less than 1:
`C = lim_{n rightarrow infty} |{n!}/{n^n}|^(1/n)`

`C = lim_(n->oo) |{(n!)^(1/n)}/n|`

Since `n! lt n^n` for `n gt 1` , `(n!)^(1/n) lt n` . Therefore this limit converges to 0, therefore the series converges.

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