摘 要本文主要探讨研究生入学考试数学试卷中与无穷级数相关的问题，在前人研究的基础上，重点分析了四川师范大学 2014-2019 年的十二套考研试卷，对其中涉及级数理论的相关试题的题型、考查的知识点进行归纳总结，侧重对数项级数的敛散性判别、幂级数的收敛域及和函数求解、函数的幂级数展开式等几类典型试题分析其解题思路与解题方法，力图达到对此类问题的掌握有所帮助的目的。关键词：研究生考试；级数；函数；幂级数；收敛AbstractThis paper mainly discusses the problems related to infinite series in the mathematics test paper of postgraduate entrance examination. Based on the previous studies, it focuses on the analysis of 12 sets of postgraduate entrance examination papers of Sichuan Normal University from 2014 to 2019, including the types of questions related to series theory and the knowledge points of examination, focusing on the convergence and divergence of the logarithmic series, the convergence domain and power series And function solution, function power series expansion and so on several kinds of typical test questions analyze their solution ideas and methods, trying to achieve the purpose of helping to grasp such problems.Key words：Graduate examination; series; function; power series; convergence目 录1 引 言····························12 级数相关知识的介绍·······················22.1 定义与相关概念······················22.2 基本定理与公式······················42.3 级数的考试内容与要求···················63 考研数学中级数相关题型的分类··················64 几类题型的解法分析·······················64.1 证明常数项级数敛散性··················64.2 幂级数的相关题型····················104.2.1 求幂级数的收敛域及其和函数············104.2.2 将函数展开成幂级数形式...
