均值不等式的八种证法

由于不等式本身在数学中的重要地位以及不等式的证明的困难性,使不等式的证明方法成为数学领域内的热门问题.本文拟将介绍均值不等式的算术归纳法、局部调整法、排序原理、不等式法、几何方法、变量替换法、归纳原理、逐次调整法等八种证明方法,归纳总结出不等式证明技巧,进而提高学习者不等式探究能力和证明方法.

Eight Proofs for Mean Inequality

Proof method for the Inequality has become a more and more hot issue within the field of mathematics because of its important role in mathematics as well as the difficulty of proof.This article introduced eight proofs for Inequality such as the method of induction by arithmetic,the method of local adjustment,ordering principle,method of inequality,geometric method,method of variable substitution,the principle of induction,method of successive adjustment,on which the skills for proof Inequality are concluded.Therefore,the exploring ability and proof methods for inequality of learners can be improved.