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  1. #1
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    Proof question

    My question Prove that 3^n > n! whenever n is a positive integer greater than 6

    Can you help me please ı can't solve this proof
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  2. #2
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    Quote Originally Posted by jacklarson View Post
    My question Prove that 3^n > n! whenever n is a positive integer greater than 6

    Can you help me please ı can't solve this proof
    Try using induction.

    Base step: n = 7

    3^7 = 2187

    7! = 5040


    The statement is clearly not true...
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by jacklarson View Post
    My question Prove that 3^n > n! whenever n is a positive integer greater than 6

    Can you help me please ı can't solve this proof
    It's 3^n<n!. Try induction or any of the other twenty applicable methods.
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  4. #4
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    Quote Originally Posted by Drexel28 View Post
    It's 3^n<n!. Try induction or any of the other twenty applicable methods.
    Just curious, what are the other methods?
    Do you mind listing them?
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  5. #5
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by novice View Post
    Just curious, what are the other methods?
    Do you mind listing them?
    Note that \frac{3^n}{n!}=\frac{3}{n}\cdots\frac{3}{n} and show that this is less than one. Prove that there is an injection from the set of all permutations of \left\{1,\cdots,n\right\} to the set of all true ordering relations on \left\{1,\cdots,n\right\}. etc.
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