Question: Given n positive integers x1, x2, ..........xn not necessarily distinct, prove that either n(x1 + x2 + + xt), for some 1 < i <

Given n positive integers x1, x2, ..........xn not necessarily distinct, prove that either n(x1 + x2 + ∙∙∙∙∙∙∙∙+ xt), for some 1 < i < n, or there exist 1 < i < j < n such that n\(xt+1 + ∙∙∙∙∙∙ +xj-1 + xj).

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