January 8th, 2015, 04:39 AM  #1 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  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'hÃ´pital, but what is the derivative of $\displaystyle \ln(n!) $? Last edited by skipjack; January 8th, 2015 at 05:57 AM. 
January 8th, 2015, 06:02 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
You could use Stirling's formula instead, so you might find it useful to look up how that is proved.


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