一类级数的求和问题  

A METHOD ABOUT CALCULATING THE SUM OF A KIND OF SERIES

作　　者：马亚利[1] 

机构地区：[1]陕西科技大学基础部,陕西咸阳7120081

出　　处：《咸阳师范学院学报》2002年第4期13-15,共3页Journal of Xianyang Normal University

摘　　要：从 f( χ) =χ在 ( - π,π)内的傅立叶级数展开式出发 ,导出形如 ∑∞n=1( - 1 ) n+ 1sin nχn2 k-1及 ∑∞n=1( - 1 ) n+ 1con nχn2 k 的三角级数的和函数的特点及函数的递推求法 ,从而解决形如∑∞n=11n2 k、∑∞n=1( - 1 ) n+ 1n2 k 、∑∞n=11( 2 n- 1 ) 2 k-1(其中 k∈ N)等级数的求和问题。According to the Fourier Series eχpansion of the function:f(χ)=χ(-π<χ<π),the sum functions of some trigonometric series like ∑∞n=1(-1) n+1 sinnχn 2k+1 and ∑∞n=1(-1) n+1 cosnχn 2k are deduced ,then the qualities of the sum functions are seen and the recursion method of getting sum function of series is obtained.Theerfore the problem of finding the sum of series ∑∞n=11n 2k ,∑∞n=1(-1) n+1 n 2k ,∑∞n=11(2n-1) 2k and ∑∞n=1(-1) n+1 (2n-1) 2k-1 (k∈N)is solved.

关 键 词：级数 求和问题 傅立叶级数 三角级数 和函数 数学归纳法 递推公式 

分 类 号：O173.1[理学—数学] O174.21[理学—基础数学]