M=1x2+2x3+3x4+··········+（n-1)xn,则M等于?
问题描述：
M=1x2+2x3+3x4+··········+（n-1)xn,则M等于?
答
M=1×2+2×3+...+(n-1)×n
=[1×2×(3-0)+2×3×(4-1)+...+(n-1)×n×((n+1)-(n-2))]/3
=(1×2×3-0×1×2+2×3×4-1×2×3+...+(n-1)×n×(n+1)-(n-2)×(n-1)×n)/3.裂项
=(n-1)n(n+1)/3 .消去中间项