证明不等式的方法多样性,是近年来高考的焦点、热点、难点.本文从突破不等式证明题的策略加以探索、研究、归纳,以共读者学习时参考.例1证明不等式1+1/21/2+1/31/2+…+1/n1/2<2n1/2(n∈N*).分析:这是一个与正整数n有关的命题,首先想到应用数学归纳法,另外还涉及不等式证明中的放缩法、构造法等.解法1:(1)当n=1时,不等式成立. The diversity of methods to prove inequality is the focus, the hot spot and the difficult point of college entrance examination in recent years.This paper explores, studies and summarizes the strategies of breaking the inequality proving questions, and makes reference to the total readers.Example 1 Prove inequality 1 + 1/21 / 2 + 1/31/2 + ... + 1 / n1 / 2 <2n1 / 2 (n∈N *). Analysis: This is a proposition related to a positive integer n, which first comes to the application of mathematical induction and to inequalities Demonstration in the scaling method, construction method, etc. Solution 1: (1) When n = 1, the inequality holds.