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Topic: proof sum has certain bound
Replies: 2   Last Post: Oct 28, 2017 5:53 AM

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steven brawer

Posts: 2
Registered: 10/27/17
proof sum has certain bound
Posted: Oct 27, 2017 5:52 PM
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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 < (N-1)/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 N-dimensional rectangle to the diagonal. But I need to show it is smaller than (N-1)/N.

It would be fine to show it is true almost everywhere.

Thank you.

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