一道数列极限竞赛题的若干解法

Investigation into a Number of Solutions to a Sequence Limit Problem in Chinese Mathematics Contest

主要借助于迫敛性,Taylor公式,Abel引理,以及Riemann积分的定义,本文深度剖析第七届全国大学生数学竞赛非数学专业类预赛试卷第一题,并基于不同视角为该题设计出七种解答方案,以期在数列极限理论的学习与教学方向带来更多思考.

Mainly by using the technique of squeeze,Taylor's formulae,Abel's lemma,and the definition of Riemann's integral,we deeply analyzes the first problem in the non-mathematics-majored group test of the 7th College Mathematics Contest of China,and design for this problem based on different perspectives,with a desire to bring in more thinking in the direction of learning and teaching sequence limit theory.