1x2x3+2x3x4+...+nxx=?

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1x2x3+2x3x4+...+nxx=?
1x2x3+2x3x4+...+nxx=?

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)

用升次裂项的方法做：
1x2x3+2x3x4+...+nxx=nxxx/4

1x2x3+2x3x4+...+nxx=? 1x2x3+2x3x4+.+nx(n+1)(n+2)=? 1x2x3+2x3x4+.+n(n+1)(n+2)=? 1x2x3+2x3x4+3x4x5+...+7x8x9=, 1x2X3+2x3X4+3x4X5+…+7X8X9=? 1x2=1|3(1x2x3-0x1x2) 2x3=1|3(2x3x4-1x2x3) 3x4=1|3(3x4x5-2x3x4)由此推断1x2x3+2x3x4+3x4x5.7x8x9=? 1x2=1/3x(1x2x3-0x1x2)2x3=1/3x(2x3x4-1x2x3)3x4=1/3x(3x4x5-2x3x4)求1x2x3+2x3x4+3x4x5+...+7x8x9=? 2/1x2x3+2/2x3x4+2/3x4x5+2/4x5x6+...+2/98x99x100= 请1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6= 1/1x2x3+1/2x3x4+1/3x4x5+------+1/98x99x100= 1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+.1/(20x21x22)=? 1/1x2x3+1/2x3x4+1/3x4x5+.+1/9x10x11= 1/1x2x3+1/2x3x4+1/3x4x5+.1/98x99x100=要有中间过程 1/1x2x3+1/2x3x4+1/3x4x5+.+1/11x12x13= 数学问题1/1x2x3+1/2x3x4+.1/48x49x50=? 1x2x3+2x3x4+3x4x5+4x5x6+...+n(n+1)(n+2)= 1X2X3+2X3X4+3X4+.+nx(n+1)(n+2)= 求和Sn=1x2x3+2x3x4+……+n(n+1)(n+2)