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Math Help - Proof Using Strong Induction

  1. #1
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    Proof Using Strong Induction

    I can't figure out this problem. Any help is appreciated.

    Suppose h0, h1, h2,..... is a sequence defined as follows:

    h0 = 1, h1 = 2, h2 = 3

    hk = hk-1 + hk-2 + hk-3 for all ints k is greater than or equal to 3.

    Prove that hn is less than or equal to 3^(n).

    Thank you!
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  2. #2
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    For n=0,1,2 you have that h_n\le 3^n. So assume the assertion is true for some n\ge{2}, then h_{n+1}=h_n+h_{n-1}+h_{n-2}\le 3^n+3^{n-1}+3^{n-2}<3\cdot 3^n=3^{n+1}.
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