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Math Help - How do I solve a limit involving factorials?

  1. #1
    s3a
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    How do I solve a limit involving factorials?

    How do I solve the following without plugging in large values of n in order to see whether the numerator or denominator wins? (in other words: how do I show work?):



    Any input would be greatly appreciated!
    Thanks in advance!
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by s3a View Post
    How do I solve the following without plugging in large values of n in order to see whether the numerator or denominator wins? (in other words: how do I show work?):



    Any input would be greatly appreciated!
    Thanks in advance!

    Notice for say n=5 that you get

    \frac{2\cdot (5!)}{4^5}=2\frac{1}{4}\frac{2}{4}\frac{3}{4}\frac  {4}{4}\frac{5}{4}

    Notice that for n > 4 that each fraction will be larger than 1.

    Now what will happen as n increases. I hope this helps.
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