极限函数与和函数的关系及其连续性  

Relation and Continuity of Limit Function and Sum Function

作　　者：杨传森[1] 

机构地区：[1]盐城纺织职业技术学院,江苏盐城224005

出　　处：《河北北方学院学报（自然科学版）》2011年第6期5-6,10,共3页Journal of Hebei North University:Natural Science Edition

摘　　要：给出极限函数与和函数的定义.讨论了极限函数与和函数之间的关系,利用极限函数得到函数项级数收敛的一个必要条件,研究了极限函数与和函数的连续性,得到部分和函数列连续的一个充分条件.This paper gives the definitions of the limit function and the sum function and discusses the relation between them. And the continuity of the limit function and the sum function are discussed. The necessary condition for convergent series is obtained by using limit function and the continuity of the limit function and the sum function is discussed as well. Finally the sufficient condition for a sequence of the continuous partial sums of the series is got.

关 键 词：极限函数 和函数 关系 连续性 

分 类 号：O173.1[理学—数学]