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数列是研究离散问题的重要数学模型,也是学习高等数学的重要基础,因而为自主招生考试试题中的必考内容。数列交汇问题往往创新性强、形式多样、内涵丰富,而且难度比较大。数列具有离散性和变量性的双重特点,在解决数列交汇问题中,函数与方程的思想、化归思想和分类思想及归纳推理、数学归纳法、待定系数法、换元法、构造法、放缩法、模型法等数学方法在解决问题中起着非常重要的作用,要引导学生在解题中用这些思想方法来指导分析转化问题去发现问题解题的思路,提高解题的效率。
The series is an important mathematical model for studying discrete problems and also an important foundation for learning advanced mathematics. Therefore, it is an indispensable part of self-enrollment examination questions. The problem of intersection of sequence is often innovative, diverse, rich in content, and more difficult. The sequence of numbers has the dual characteristics of discreteness and variable nature. In solving the sequence intersection problem, the thought of function and equation, thought of categorization and classification, inductive inference, mathematical induction, undetermined coefficient method, Mathematical methods such as shrinking method and model method play a very important role in solving problems. Students should be guided to use these methods to guide the analysis of transformation problems in order to find out the solutions of problems and improve the efficiency of problem solving.