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.
作者
杨传富
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)
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)。
关键词
傅里叶级数
交错级数
创新能力
fourier series
alternating series
innovation ability
