Generalization of H. Alzer’s Inequality

Using the mathematical induction and Cauchy’s mean-value theorem, for any positive number r, we prove that n qn qm qkk- n1 nisqkkq1 irrnq1m nisqkmqq1kir.1r r, where n and m are natural numbers, k is a nonnegative integer. The lower bound is best possible. This inequality generalizes the Alzer’s inequality w J. Math. Anal. Appl. 179 1993., 396]402x. An open problem is proposed