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January 8th, 2015, 04:39 AM   #1
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limit with factorial.

Prove that $\displaystyle \lim_{n \to \infty} \sqrt[n]{n!} = \infty$

According to me it is equal to $\displaystyle e^{\lim_{n \to \infty} \frac{\ln(n!)}{n}}$ so I would need to use l'hôpital, but what is the derivative of $\displaystyle \ln(n!) $?

Last edited by skipjack; January 8th, 2015 at 05:57 AM.
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January 8th, 2015, 06:02 AM   #2
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You could use Stirling's formula instead, so you might find it useful to look up how that is proved.
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factorial, limit

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