1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+.1/(20x21x22)=?

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1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+.1/(20x21x22)=?

1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+.1/(20x21x22)=?
1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+.1/(20x21x22)=?

1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+.1/(20x21x22)=?
1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+.1/(20*21*22)
=1/2[1/1*2-1/2*3]+1/2[1/2*3-1/3*4]+1/2[1/3*4-1/4*5]+...+1/2[1/20*21-1/21*22]
=1/2[1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+...+1/20*21-1/21*22]
=1/2[1/2-1/21*22]
=1/2*115/231
=115/462

1x2x3+2x3x4+...+nxx=? 1/1x2x3+1/2x3x4+.+1/98x99x100 . 1/1X2X3+1/2X3x4+…+1/48X49X50 1X2X3+2X3X4+.+n(n+1)(n+2) 1x2x3+2x3x4+.+nx(n+1)(n+2)=? 1x2x3+2x3x4+.+n(n+1)(n+2)=? 求和1x2x3+2x3x4+...+n(n+1)(n+2) 1x2x3+2x3x4+…+n(n+1) 1x2x3+2x3x4+3x4x5+…+8x9x10 1x2x3+2x3x4+3x4x5+.+10x11x12 1x2x3+2x3x4+3x4x5+...+7x8x9=, 1x2X3+2x3X4+3x4X5+…+7X8X9=? 1x2x3 2x3x4 3x4x5 .10x11x12,怎么算 求和：1X2X3+2X3X4+3X4X5+...+98X99X100 计算1x2x3+2x3x4+…+48x49x50 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=? 1/1x2x3+1/2x3x4+1/3x4x51/2x3x4 + 1/3x4x5 + 1/4x5x6 +……+1/99x100x101是 1/（2x3x4）