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    how would I work out the limit as n tends to infinity of n!/n^n
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    Note that  0<\frac{n!}{n^n} = \frac{n}{n} \cdot \frac{n-1}{n}\cdot \ldots \frac{2}{n}\cdot \frac{1}{n} \leq \frac{1}{n} .
    What happens to 1/n and what can you then say about  n!/n^n .
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    There is actually a nice consequence of this result you can use it to show that  (n!)^\frac{1}{n} \rightarrow \infty .
    Proof
    Exercise... \square
 
 
 
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