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Math Help - Proof Using Strong Induction

  1. #1
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    Proof Using Strong Induction

    Can anyone help me get started with the proof attached. I have to use strong induction.
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  2. #2
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    Quote Originally Posted by jgm51672 View Post
    Can anyone help me get started with the proof attached. I have to use strong induction.
    Check the base case (for simplicity make the base case all n up to 6), I will assume you have done so.

    Now suppose for some k>6 that: for all 0 < r \le k that T(r)<4n

    Now consider:

    T(k+1)=T(\lfloor (k+1)/3 \rfloor)+T(\lfloor (k+1)/5 \rfloor)+T(\lfloor (k+1)/7 \rfloor)+(k+1)

    which by assumption:

    ............. <\frac{4(k+1)}{3}+\frac{4(k+1)}{5}+\frac{4(k+1)}{7  }+(k+1)

    Now you should be able to finish this yourself.

    CB
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    Thank you

    kindly.
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