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数列与不等式是数学高考的重要考查内容,而两者的综合考查又是高考的重要形式之一.它们与函数、推理等知识和技能相互交汇,可有效考查学生的基础知识掌握与运用能力,是数学高考题中一道亮丽的风景线.本文通过近年来数列不等式的证明,归纳总结出这类问题的常见处理策略,以期给同学们的学习带来启迪与帮助.一、放缩法放缩法是中学不等式证明的常用方法,在数列不等式证明过程中通过放缩,可与等差、等比数列求和相联系,或与裂项求和等技巧相结合,以有效降低问题求解的难度.
The series and the inequality are the important contents of the math entrance examination, and the comprehensive examination of the two is one of the important forms of the college entrance examination.They interact with the knowledge and skills such as the function and reasoning, which can effectively check the students’ ability of mastering and using the basic knowledge, Is a beautiful landscape of the math entrance exam.This paper summarizes the common treatment strategies of such problems through the identification of numerical inequalities in recent years in order to bring enlightenment and help to the students learning.First, Is a commonly used method to prove inequality in middle school. It can be linked with equalization and equalization sequence summaries through shrinking and contraction in the process of numerical inequalities, or combined with the techniques of summation of cracked items to effectively reduce the difficulty of solving problems.