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《数学通报》1997年第7期的征解问题是:设x_i>0(i=1,2,…,n,n≥3),证明或否定(记 S=x_1常新德老师在《中学数学教学参考》2004年第11期上给出了此题的一个归纳法证明.笔者分析此题的结构和形式,其不等式左边是乘积和的形式,因而采取排序原理可以得到更简捷更实质性的证明.其实此题的本质还是反映了排序原理,并且据此原理此题还可以深化和拓展,有兴趣的读者不妨一试.下面给出一个证明:
The problem of solicitation of No. 7 of 1997 of Mathematical Bulletin is: Suppose x_i> 0 (i = 1, 2, ..., n, n≥3), prove or negate (note S = x_1) Mathematics teaching reference "on the 11th of 2004 is given a proof of induction of this issue.The author analyzes the structure and form of the problem, the left side of the inequality is the product of the form and therefore the principle of sorting can be more simple and more substantive In fact, the essence of this question still reflects the principle of sorting, and according to the principle of this question can also be deepened and expanded, interested readers may wish to try. Here is a proof: