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Math Help - Recusive Definition

  1. #1
    Newbie Phat32's Avatar
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    Recusive Definition

    I am really confused on how to do recursive definitions. The question is:

    n! >= 3^n for every Integer n >=7

    The textbook I have really doesn't explain how to solve for it and I am hoping someone can explain how I prove for it. can someone please explain how you solve for these type of equations? Thanks!

    EDIT: I forgot to mention that we are using Mathematical Induction.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Phat32 View Post
    I am really confused on how to do recursive definitions. The question is:

    n! >= 3^n for every Integer n >=7

    The textbook I have really doesn't explain how to solve for it and I am hoping someone can explain how I prove for it. can someone please explain how you solve for these type of equations? Thanks!

    EDIT: I forgot to mention that we are using Mathematical Induction.
    Use induction with n=7 as a base case, then show that if for some k:

    k!\ge 3^k

    then

    (k+1)! \ge 3^{k+1}

    CB
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