摘要
借助函数fk(x)=π/2xk(k为自然数)在(-π,π]上的Fourier级数展开式,本文总结出当p为偶数时p级数∞∑(n=1)1/np和交错级数∞∑(n=1)((-1)n-1)/np的两个求和公式,以及当k为奇数时∞∑(n=1)((-1)n)/((2n+1)k)的求和公式.
Based on Fourier series of the function fk（ x ） = π/2 xk（k ∈ N＋,0 ≤ x ≤ π）,This paper sums up two summation formulas of P-series ∞∑（n=1）1/np and alternating series ∞∑（n=1）（（-1）n-1）/np when P is an even number and the summation formula of alternating series ∞∑（n=1）（（-1）n）/（（2n＋1）k）when K is an odd number.
出处
《河西学院学报》
2009年第5期5-10,共6页
Journal of Hexi University
