与自然数n有关的不等式,我们常规的思考方法是数学归纳法证明.但有些问题用常规的思维方式寻求解题途径却比较繁琐,甚至无从着手.在这种情况下,如果我们改变思维方向,换个角度思考,往往就能找到一条绕过障碍的新途径.构造法就是这样的手段之一.笔者通过研究,发现利用数列的单调性证明数学问题,更加简单明晰,现抛砖引玉,希望此种方法能够被学生掌握. The inequality associated with the natural number n, our conventional way of thinking is proved by mathematical induction. But some problems using conventional ways of thinking to find ways to solve problems are more tedious and even impossible to start. In this case, if we change the direction of thinking, Thinking from another perspective, you can often find a new way to get around the obstacles. The construction method is one of the means. Through the research, the author finds that using the monotony of the series to prove the mathematical problem is more simple and clear, and it is hoped that this method will be introduced. Can be mastered by students.