一道大学生数学竞赛题目的一题多解探讨

Discussion on Multiple Solutions of One Problem in a College Mathematics Contest

摘要: 本文给出了一道1975年苏联大学生数学竞赛极限问题的七种不同解法，使读者从处理极限的多个不同角度出发去解决问题，一方面熟悉关于极限的多个知识点，达到融会贯通；另一方面能拓宽解题思路，培养和提高从多个角度解决实际问题的能力，达到举一反三。对于培养学生学习高等数学的兴趣和参加国内大学生数学竞赛也有很好的促进作用。

Abstract: This paper gives seven different solutions to the limit problem of the 1975 Soviet Union College Students' mathematics competition, which enables readers to solve the problem from many dif-ferent angles of dealing with the limit. On the one hand, they are familiar with many knowledge points about the limit, so as to achieve mastery; on the other hand, it can broaden the thinking of solving problems, cultivate and improve the ability to solve practical problems from multiple angles, so as to draw inferences from one instance. It also plays a very good role in cultivating students’ interest in learning higher mathematics and participating in domestic college students’ mathematics competition.