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Math Help - How do I show that this limit goes to infinity?

  1. #1
    s3a
    s3a is offline
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    How do I show that this limit goes to infinity?

    In the limit:

    lim as n--->inf 2*(n!)/4^n = 2*lim as n--->inf (n!)/4^n

    how do I show that n! grows faster than 4^n?

    This is not a proof question. It's just a "do it" question and I'm asking for the "how".

    The answer:
    =infinity

    Any input would be greatly appreciated!
    Thanks in advance!
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  2. #2
    Member
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    Quote Originally Posted by s3a View Post
    In the limit:

    lim as n--->inf 2*(n!)/4^n = 2*lim as n--->inf (n!)/4^n

    how do I show that n! grows faster than 4^n?

    This is not a proof question. It's just a "do it" question and I'm asking for the "how".

    The answer:
    =infinity

    Any input would be greatly appreciated!
    Thanks in advance!
    Ratio Test works great here.

     \lim_{n\rightarrow\infty} \frac{|a_{n+1}|}{|a_{n}|}

    Or you can just plug it into your calculator for the "how" part. 2*50! / 4^50 = 4.798 x 10^34
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