一类交错级数求和的探讨及其推广  

On the Summation of a Class of Alternating Series and Its Extension

作　　者：杨传富[1] 代成 YANG Chuanfu;DAI Cheng(Department of Applied Mathematics,Nanjing University of Science and Technology,Nanjing 210094,China;Propaganda Department,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学应用数学系,南京210094 [2]南京理工大学宣传部,南京210094

出　　处：《大学数学》2021年第6期65-67,共3页College Mathematics

基　　金：国家自然科学基金(11871031)。

摘　　要：借助傅里叶级数展开为工具,探讨一类交错级数∑_(n=1)^(∞)(-1)^(n-1)/(2n-1)^(3)的求和问题.进一步推广给出级数∑_(n=1)^(∞)(-1)^(n-1)/(2n-1)^(2k-1)的和,教学中通过对问题引申培养学生的创新能力.This paper uses the Fourier series expansion as a tool,and discusses the summation of a class of alternating series ∑_(n=1)^(∞)(-1)^(n-1)/(2n-1)^(3).Furthermore,the summation of series ∑_(n=1)^(∞)(-1)^(n-1)/(2n-1)^(2k-1) is given.In teaching,students′innovation ability is cultivated by the extending problems.

关 键 词：傅里叶级数 交错级数 创新能力 

分 类 号：O174.21[理学—数学]