1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6---------+1/48*49*50

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1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6---------+1/48*49*50
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1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6---------+1/48*49*50
1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6---------+1/48*49*50

1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6---------+1/48*49*50
=1/2×(1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+……+1/48*49-1/49*50)
=1/2×(1/1*2-1/49*50)
=306/1225

1/2(1/N(N+1)-1/(N+1)(N+2))=1/N(N+1)(N+2)
然后代入1 2 3....销项即可

1+2+3+4+1 1 2 3 4 1 2 3 4 1 2 3 4 1,2,3,4, 1 2 3 4 1 2 3 4 1,2,3,4, 1,2,3,4, 1,2,3,4, 1,2,3,4, 1 2 3 4 1,2,3,4, 1,2,3,4, 1,2,3,4, 1、2、3、4 1+2+3×4 1,2,3,4