例说n项和数列极限的几种求法  

Several Explorations in Resolving Limit of Number Sequence of the Sum of n Terms by Examples

作　　者：何美[1] 刘小川[1] 

机构地区：[1]山西大同大学数学与计算机科学学院,山西大同037009

出　　处：《高等数学研究》2016年第3期37-39,共3页Studies in College Mathematics

基　　金：山西大同大学教改课题项目(XJG2015201)

摘　　要：有限个数列和的极限一般可用"数列和的极限等于数列极限的和"的运算法则来计算,而对于n项和数列的极限不能采用和的运算法则.针对此问题,文中利用迫敛性、定积分、幂级数和函数性质以及Fourier级数和函数得到了求此类极限的方法.To calculate the limit of the sum of limited sequence always uses the rule ＇ the limit of the sum equals the sum of the limit＇ , but this rule cannot resolve the limit of the number sequence of the sum of n terms. Given several methods using squeeze theorem, definite integral, properties of sum function of power series and the sum function of Fourier series to resolve such limit.

关 键 词：n项和数列 迫敛性 定积分 幂级数 FOURIER级数 

分 类 号：O171[理学—数学]