Abstract
We prove: If A n and G n (respectively, A′ n and G′ n ) denote the weighted arithmetic and geometric means of x 1,…, x n (respectively, 1 − x 1,…,1 − x n ), where x i ϵ (0, 1 2 ] (i = 1,…, n; n ≥ 2) are real numbers which are not all equal, then we have min 1≤i≤n x i 1-x i < A′ n−G′ n A n < max 1≤i≤n x i 1−x i .
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