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Math Help - Limit involving log & factorial

  1. #1
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    Limit involving log & factorial

    Hi,

    I have a problem finding the following limit:

    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
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  2. #2
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    Re: Limit involving log & factorial

    Quote Originally Posted by Omegacc View Post
    I have a problem finding the following limit:
    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: \log \left[ {\left( {3^2 } \right)!} \right] = \sum\limits_{k = 1}^9 {\log (k)}
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  3. #3
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    Re: Limit involving log & factorial

    Thanks, but then I get stuck on \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)}}
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    Re: Limit involving log & factorial

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