摘 要许多中学生在数学归纳法在不等式的应用上都相对薄弱，在一部分学生中也是似懂非懂，按部就班的使用，并不能清楚的知道其原理，所以数学归纳法反而成了失分率非常高的知识点。那么如何学好它呢？我们应当从数学归纳法的历史及其发展入手，这是学会归纳法的关键，也是教师能够更好授课的前提。然而题型变化多端，如果学生对其类型了解的不够，将导致不能正确地选择解题方法。因此，如何全面的分析和研究面对各类题型采取的解题方法不同的问题，是当前学生学习并运用归纳法的关键，这也是本文的重点。本篇论文主要通过了解数学归纳法的概念和原理总结了一些常用的证明方法：放缩传递法、反证法、比较法、加减对消法、循环法、综合法；并分析了学生常见错误的原因；提出了一些有建设性地建议。关键词：数学归纳法；不等式；中学数学AbstractMany middle school students are relatively weak in the application of mathematical induction in inequality, in some students are also vaguely understood, step-by-step use, and can’t clearly know its principle, so mathematical induction has become a very high loss rate of knowledge. So how to learn it well? We should start with the history and development of mathematical induction, which is the key to learning induction and the premise for teachers to teach better. However, the question types vary a lot, if the students do not know enough about its types, will lead to the problem can’t choose the correct method. Therefore, how to comprehensively analyze and study the different problem solving methods adopted for various types of questions is the key for students to learn and apply induction method, which is also the focus of this paper. This paper mainly through understanding the concept and principle of mathematical induction summarizes some commonly used methods of proof, including reduction method, transfer method, reduction method, comparison method, addition and subtraction pair elimination method, circulation ...
