Research on solving sequence summation problems in mathematical competitions
数学竞赛中解决数列求和问题的研究

摘要

数列是高中数学三条知识主线其一的几何与代数中的重要内容，通过对数列的学习可以加深学生对函数问题的理解，也为未来高等数学中的级数，分部积分法等相关内容的学习做好铺垫。数列求和作为数列中最常见的问题，不仅是高考的重要考查内容，也在数学竞赛中占据重要地位，本文结合实例梳理了数学竞赛和高考真题中数列求和问题的解题方法与策略，并给出对高中数学竞赛教师在数列求和解题专题教学和学生解题方法学习的建议。

Abstract

Series is an important part of geometry and algebra, one of the three main knowledge lines of high school mathematics. Learning series can deepen students' understanding of function problems, and pave the way for the future study of series, integration by parts and other related content in higher mathematics. As the most common problem in the series of numbers, summation is not only the important content of the college entrance examination, but also occupies an important position in the mathematics competition. This paper combing through the methods and strategies of solving the series summation problems in the math competition and the college entrance examination, and gives some suggestions for teachers in the senior high school mathematics competition in the thematic teaching of series summation problems and students' learning of problem-solving methods.