Keyword: «the cauchy inequality»

The article is devoted to a new proof of the generalized Cauchy inequality for arithmetical and geometrical mean of positive numbers, using the method of forward and backward induction. We give examples of simple and generalized Cauchy inequalities to solve problems of high levels of school mathematics

The article is devoted to a proof of the generalized Cauchy inequality for arithmetical and geometrical mean of positive numbers, realized by the method of forward and backward induction. We give examples of the generalized Cauchy inequality to solve problems