数列极限几个简单结论的推导

易强 吕希元

摘 要 数列极限是指随着的无限增大，无限接近于某个任意常数的结果，它体现了一个极限过程，本文主要讨论在数列极限的定义和它的个重要性质的基础上延伸出了几个结论，并对结论加以证明。

关键词 数列极限 收敛 邻域 发散 有界数列

中图分类号：O171 文献标识码：A DOI：10.16400/j.cnki.kjdks.2016.07.020

Abstract Limit of a sequence refers to with the infinitely increasing， infinitely close to the results of an arbitrary constant， it reflects a limiting process. This paper mainly discusses on the basis of the definition of the limit of a sequence and its important properties extends several conclusions， and the conclusion is proved.

Keywords： sequence limit； convergence； neighborhood； divergence； bounded sequence