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《数学通报》2008年第12期刊出1765号问题的解答,问题的提出者巧妙地构造幂级数,实现了问题的证明.事实上,幂级数法不仅可以用来证明不等式,而且可以用于发现新的不等式,见文献[1].本文先介绍幂平均不等式,再应用其推论将1765号问题的结论进行加强,最后利用幂级数法,配合以幂平均不等式的推论,给出《数学通报》历年来刊出的一组条件不等式的统一证明.1幂平均不等式及其推论
Journal of Mathematical Sciences, 2008 Issue 12, No. 1765 presents a solution to the question No. 1765, in which the proponent of the problem skillfully constructs the power series and proves the problem. In fact, the power series method can be used not only to prove inequalities, In discovering the new inequality, see [1] .This paper first introduces the power-average inequality, and then applies its inference to strengthen the conclusion of the 1765th issue. Finally, using the power series method, with the inference of the power-mean inequality, A Unified Proof of a Set of Conditional Inequalities Published in Mathematics Bulletin over the Years. Power Inequality and Inference