Comparative method? ① Difference comparison method: press A-B > 0<a>b, want to prove it? A>b, as long as it proves that A-B > 0; ? ② business comparison method: according to a/b= 1, when b >; 0, have to? a & gtb； When b>0 proves a>b, just prove A/B >; 1; What time? b & lt0? When, have to? A< B. Comprehensive method? Cause leads to result. When proving inequalities, from the known inequalities? According to the conditions of the problem, apply the nature of inequality and make appropriate changes. Form to derive the inequality to be proved, and the legal method is also called positive proof? Or the method of inducing fruit. ? Analytical method? When fruit-holding hormone proves inequality, from the proposition to be proved? Hair, looking for sufficient conditions to make it established. Because of "analysis" It's not very convenient to write a certificate, so sometimes we can benefit? Find a way to prove the problem through analysis. And then use the "comprehensive method" to enter? Line expression. Scaling method? Appropriately enlarge or reduce the unequal sides to realize the proof? Purpose. ? Mathematical induction? When proving the inequality related to the natural number n, it can be mathematically simplified as? Nafa proved it. ? To prove inequality by mathematical induction, we should pay attention to two steps and one conclusion. Open. ? When proving the second step, comparison method and scale method are generally used. Methods and analytical methods. ? Reduction to absurdity? When proving inequalities, suppose that the propositions to be proved are opposite? Face is established, combine it with other conditions as one condition? Use known definitions, theorems, axioms and other basic principles? Gradually deduce the conditions of a proposition or the certainty of proof? What should I say to the conclusion that reason or accepted simple facts contradict each other? The conclusion of the Ming Yuan hypothesis is not valid, thus affirming the alternative method of the original proposition? The purpose of substitution is to reduce the number of variables in inequality. In order to make the problem difficult and simplify it, change the commonly used elements? There are trigonometric substitution and algebraic substitution. ? Tectonic method? By constructing functions, graphs, equations,? Sequences, vectors, etc? Prove inequality.