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Math Help - need help

  1. #1
    Junior Member
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    Nov 2008
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    need help

    floor function: the largest integer < x

    Show:
    1+ 2 + … + 2^(d-1) + 1 ≤ n if d = floor(log(base2)n)
    help me please.....
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  2. #2
    MHF Contributor
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    Quote Originally Posted by tukilala View Post
    floor function: the largest integer < x

    Show:
    1+ 2 + + 2^(d-1) + 1 ≤ n if d = floor(log(base2)n)
    help me please.....
    Hi

    1+ 2 +  + 2^{d-1} = \sum_{k=0}^{d-1} 2^k = \frac{2^d-1}{2-1} = 2^d-1

    Therefore

    1+ 2 +  + 2^{d-1}+1 = 2^d
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