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Math Help - Six real numbers

  1. #1
    MHF Contributor alexmahone's Avatar
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    Six real numbers

    A computer programmer claims that he generated six real numbers a_1, a_2, \cdots, a_6 so that the sum of any four consecutive a_i's is positive, but the sum of any 3 consecutive a_i's is negative. Prove that his claim is false.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: Six real numbers

    I think I got it.

    a1+a2+a3<0 and a1+a2+a3+a4>0
    imply a4>0
    Similarly a5>0 and a6>0

    a4+a5+a6>0 (Contradiction)
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