1乘2乘3分之1+2乘3乘4分之1+...+98乘99乘100分之1
=1/(1x2x3)+1/(2x3x4)+……+1/(98x99x100)
=(1/2)[2/(1x2x3)+2/(2x3x4)+……+2/(98x99x100)]
=(1/2){[1/(1x2)-1/(2x3)]+[1/(2x3)-1/(3x4)+……+[1/(98x99)-1/(99x100)]}
=(1/2)[1/(1x2)-1/(99x100)]
=(1/2)(1/2-1/9900)
=(1/2)(4950/9900-1/9900)
=(1/2)(4949/9900)
=4949/19800
=0.24994949494949494949494949494949