# Limit involving log & factorial

• Nov 1st 2012, 09:27 AM
Omegacc
Limit involving log & factorial
Hi,

I have a problem finding the following limit:

$\displaystyle lim_{n\rightarrow\infty}\frac{|log(n^2!)|}{|log((n +1)^2!)|}$.

I don't know how to get rid of the factorials in the arguments.
Any help appreciated, thanks in advance :)
• Nov 1st 2012, 09:41 AM
Plato
Re: Limit involving log & factorial
Quote:

Originally Posted by Omegacc
I have a problem finding the following limit:
$\displaystyle lim_{n\rightarrow\infty}\frac{|log(n^2!)|}{|log((n +1)^2!)|}$.
I don't know how to get rid of the factorials in the arguments.

Hint: $\displaystyle \log \left[ {\left( {3^2 } \right)!} \right] = \sum\limits_{k = 1}^9 {\log (k)}$
• Nov 1st 2012, 10:13 AM
Omegacc
Re: Limit involving log & factorial
Thanks, but then I get stuck on $\displaystyle \frac{1}{1+lim_{n\to\infty}\frac{\sum_{k=n^2+1}^{( n+1)^2}log(k)}{\sum_{k=1}^{n^2}log(k)}}$ (Thinking)
• Nov 1st 2012, 08:47 PM
Salahuddin559
Re: Limit involving log & factorial