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proof sum has certain bound
Posted:
Oct 27, 2017 5:52 PM


let <x> = mean of x(1),X(2),...,x(N), each X(i) is a real number, any value. Let q(i) = x(i)  <x>. Prove, for N > 2, that
q(i)**2/sum(i)q(i)**2 < (N1)/N
Please prove this, or direct me to an existing proof.
The expression is < 1, because it is the square of the ratio of the side of an Ndimensional rectangle to the diagonal. But I need to show it is smaller than (N1)/N.
It would be fine to show it is true almost everywhere.
Thank you.



