Feng Qi, Lokenath Debnath, "On a new generalization of Alzer's inequality", International Journal of Mathematics and Mathematical Sciences, vol. 23, Article ID 698020, 4 pages, 2000. https://doi.org/10.1155/S0161171200003033
On a new generalization of Alzer's inequality
Let be an increasing sequence of positive real numbers. Under certain conditions of this sequence we use the mathematical induction and the Cauchy mean-value theorem to prove the following inequality: , where and are natural numbers and is a positive number. The lower bound is best possible. This inequality generalizes the Alzer's inequality (1993) in a new direction. It is shown that the above inequality holds for a large class of positive, increasing and logarithmically concave sequences.
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