The Application Of Cauchy Inequality And Sequence Inequality In High Mathematics

The Cauchy inequality and Sequence inequality are two very important inequalities, which is widely used in higher mathematics, such as the extremum problem, the vector of linear algebra problems. In addition the two inequalities can also used in elementary mathematics, especially in the aspect of application, such as derivation of other inequalities, solving the variable value, the proof of inequality, the solution set of the equation and the trigonometric problems and so on. After the new curriculum, the two inequalities are absorbed into high school mathematics elective4-5inequality. More and more mathematical problems can be solved by the Cauchy inequality and Sequence inequality. It can make some basis but complex mathematical problems, the college entrance examination, competition problems easier to solve.Therefore, this article will give three kinds of contents, firstly, it will give the general form of Cauchy inequality and its four major variants, at the same time,stating the thinking of variants, then summed up several questions which can be solved by Cauchy inequality and stressed some points of teaching. Secondly,the contents is about Sequence inequality. Finally, summarized the educational value from the Cauchy inequality and Sequence inequality.In a word, if we can use the Cauchy inequality and Sequence inequality flexibility through some skills, in large part,it can reduce the difficulty of problems and improve the efficiency of solving problems. Finally, students can gain a sense of achievement.