用整数裂项因为 -n(n+1)=1/3[(n-1)n(n+1)-n(n+1)(n+2)]所以原式=1/3[0x1x2-1x2x3+1x2x3-2x3x4+...+(n-1)n(n+1)-n(n+1)(n+2)]=-1/3n(n+1)(n+2)望采纳，谢谢
