1x2=1/3x(1x2x3-0x1x2)2x3=1/3x(2x3x4-1x2x3)3x4=1/3x(3x4x5-2x3x4)由以上三个等式相加,可得：1x2+2x3+3x4=1/3x3x4x5=20读完以上材料,请你计算下列各题：1x2+2x3+3x4+…+10x11(写过程)1x2+2x3+3x4+…+nx(n+1)1x2X3+2x3X4+3x4X5+…+7X8

Question

1x2=1/3x(1x2x3-0x1x2)
2x3=1/3x(2x3x4-1x2x3)
3x4=1/3x(3x4x5-2x3x4)
由以上三个等式相加,可得：
1x2+2x3+3x4=1/3x3x4x5=20
读完以上材料,请你计算下列各题：
1x2+2x3+3x4+…+10x11(写过程)
1x2+2x3+3x4+…+nx(n+1)
1x2X3+2x3X4+3x4X5+…+7X8X9=?

Answer 1

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