计算1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100

1/(1*2*3) = (3-2)/(1*2*3) = 1/(1*2) - 1/(2*3)
同理,1/(2*3*4) = 1/(2*3) - 1/(3*4)
由此类推,得
1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100
= 1/(1*2) - 1/(2*3) + 1/(2*3) - 1/(3*4) + 1/(3*4) - 1/(4*5)+……+ 1/(98*99) - 1/(99*100)
= 1/(1*2) - 1/(99*100)
= 4949/9900
≈ 0.4999