1/1x2x3+1/2x3x4+1/3x4x51/2x3x4 + 1/3x4x5 + 1/4x5x6 +……+1/99x100x101是 1/(2x3x4)

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1/1x2x3+1/2x3x4+1/3x4x51/2x3x4+1/3x4x5+1/4x5x6+……+1/99x100x101是1/(2x3x4)1/1x2x3+1/2x3x4+1/3x4x51/2x3

1/1x2x3+1/2x3x4+1/3x4x51/2x3x4 + 1/3x4x5 + 1/4x5x6 +……+1/99x100x101是 1/(2x3x4)
1/1x2x3+1/2x3x4+1/3x4x5
1/2x3x4 + 1/3x4x5 + 1/4x5x6 +……+1/99x100x101
是 1/(2x3x4)

1/1x2x3+1/2x3x4+1/3x4x51/2x3x4 + 1/3x4x5 + 1/4x5x6 +……+1/99x100x101是 1/(2x3x4)
解1/(1+2+3)+1/(2+3+4)+1/(3+4+5)……+1/(99+100+101)
=1/6+1/9+1/12+1/15.+1/300
=1/3*(1/2+1/3.+1/99+1/100)
=1/3*4.18737751763961
=1.39579250587987