Given n positive integers x1, x2, ..........xn not necessarily distinct, prove that either n(x1 + x2 +

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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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