神马作文网1x2x3+2x3x4+...+nxx=?
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/10/07 18:20:08
1x2x3+2x3x4+...+nxx=?
1x2x3+2x3x4+...+nxx
=1/4×[1×2×3×(4-0)+2×3×4×(5-1)+.+(n-1)×n×(n+1)×((n+2)-(n-2))
+n×(n+1)×(n+2)×((n+3)-(n-1))]
=1/4×[1×2×3×4-1×2×3×0+2×3×4×5-1×2×3×4+.+(n-1)×n×(n+1)×(n+2)-(n-1)×n×(n+1)×(n-2)+n×(n+1)×(n+2)×(n+3)-n×(n+1)×(n+2)×(n-1) ]
（内部全部抵消!）
=1/4×n×(n+1)×(n+2)×(n+3)
=1/4×[1×2×3×(4-0)+2×3×4×(5-1)+.+(n-1)×n×(n+1)×((n+2)-(n-2))
+n×(n+1)×(n+2)×((n+3)-(n-1))]
=1/4×[1×2×3×4-1×2×3×0+2×3×4×5-1×2×3×4+.+(n-1)×n×(n+1)×(n+2)-(n-1)×n×(n+1)×(n-2)+n×(n+1)×(n+2)×(n+3)-n×(n+1)×(n+2)×(n-1) ]
（内部全部抵消!）
=1/4×n×(n+1)×(n+2)×(n+3)
1x2X3+2x3X4+3x4X5+…+7X8X9=?
1x2x3+2x3x4+3x4x5+...+7x8x9=,
1x2=(1/3)(1x2x3-0x1x2) 3x4=(1/3)(3x4x5-2x3x4) 问1x2x3+2x3x4+.
1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+.+1/48x49x50=
1/1x2x3+1/2x3x4+1/3x4x5+.+1/11x12x13=
1/1x2x3+1/2x3x4+1/3x4x5+.+1/9x10x11=
请1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6=
1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+.1/(20x21x22)=?
1/1x2x3+1/2x3x4+1/3x4x5+.1/98x99x100=
根号[(1x2x3+2x4x6+...+nx2nx3n)/(1x3x4+2x6x8+...+nx3nx4n)）=?
1x2x3+2x3x4+3x4x5+4x5x6+...+n(n+1)(n+2)=
1/1x2x3+1/2x3x4+1/3x4x5