A computer programmer claims that he generated six real numbers so that the sum of any four consecutive 's is positive, but the sum of any 3 consecutive 's is negative. Prove that his claim is false.

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- Aug 21st 2011, 12:22 AMalexmahoneSix real numbers
A computer programmer claims that he generated six real numbers so that the sum of any four consecutive 's is positive, but the sum of any 3 consecutive 's is negative. Prove that his claim is false.

- Aug 21st 2011, 12:35 AMalexmahoneRe: 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)