1x2+2x3+3x4+…+10x11
=1/3x(1x2x3-0x1x2)+1/3x(2x3x4-1x2x3)+1/3x(3x4x5-2x3x4)+.+1/3x(10x11x12-9x10x11)
=1/3x(1x2x3-0x1x2+2x3x4-1x2x3+3x4x5-2x3x4+.+10x11x12-9x10x11)
=1/3x(10x11x12-0x1x2)
=1/3x(10x11x12)
=440
1x2+2x3+3x4+…+nx(n+1)
=1/3x(1x2x3-0x1x2)+1/3x(2x3x4-1x2x3)+1/3x(3x4x5-2x3x4)+.+1/3x(nx(n+1)x(n+2)-(n-1)xnx(n+1))
=1/3x(1x2x3-0x1x2+2x3x4-1x2x3+3x4x5-2x3x4+.+nx(n+1)x(n+2)-(n-1)xnx(n+1))
=1/3x(nx(n+1)x(n+2)-0x1x2)
=1/3xnx(n+1)x(n+2)
第三个就利用(n-1)xnx(n+1)=n的三次方减去n