高等数学与初等数学的联系——以数列为例

The Connection between Advanced Mathematics and Elementary Mathematics—Taking the Sequence of Number as an Example

摘要: 初等数学是高等数学的基础，高等数学是初等数学的继续和提高。本研究主要分析了高等数学与初等数学知识之间的关系以及高等数学对初等数学教学的指导意义，高等数学知识内容较多地出现于数学竞赛问题之中，以2道数学竞赛中数列问题为例，以高等数学范畴中的思想和方法为解决契机，给出高中数学教学的建议。

Abstract: Elementary mathematics is the basis of advanced mathematics, while advanced mathematics is the continuation and improvement of elementary mathematics. This research mainly analyzes the relationship between advanced mathematics and elementary mathematics knowledge and the guiding significance of higher mathematics to elementary mathematics teaching, the content of advanced mathematics knowledge appears in mathematics competition problems, takes the problem of sequence of number in two mathematical competitions as an example, taking the ideas and methods in the category of advanced mathematics as a turning point, this paper gives some suggestions on the teaching of high school mathematics.