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Math Help - math induction

  1. #1
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    math induction

    Prove that n! > 2^n for every integer n greather than or equal to 4.

    This is what I have so far.

    Proof: Since 4! > 2^4 the statement is true for n greater than or equal to 4. Assume k!>2^k for some positive integer k. Observe: (k+1)! > 2^(k+1).

    I am doing okay with math induction with equal signs and not greater or less than signs. Can any one help?
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  2. #2
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    Assume that K>4 and that we know that (K!)>2^K.
    Look at (K+1)!=(K+1)(K!) !)>(K+1)2^K>(4)2^K>2^(K+1)
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  3. #3
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    Quote Originally Posted by Plato View Post
    Assume that K>4 and that we know that (K!)>2^K.
    Look at (K+1)!=(K+1)(K!) !)>(K+1)2^K
    I follow you up to this point. How did you come up with (k+1)2^k?
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  4. #4
    Senior Member ecMathGeek's Avatar
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    We have:
    k + 1 > 4
    k! > 2^k

    We assume:
    (k + 1)! > 2^(k + 1)
    (k + 1)k! > 2*2^k

    From this we get:
    (k + 1)k! > 4k! > 4*2^k > 2^(k+1)
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