=(1-1/2)+(1-1/3)+(1-1/4)+…+(1-1/100)
=1*99-(1/2+1/3+…1/100)
=99+617/147
=7327/71
1*2分之1+2*3分之1+3*4分之1......98*99分之1+99*100分之1
=1/(1*2)+1/(2*3)+1/(3*4)........+1/(98*99)+1/(99*100)
=1-1/2+1/2-1/3+1/3-1/4+........+1/98-1/99+1/99-1/100
=1-1/100
=99/100
1*2分之1+2*3分之1+3*4分之1......98*99分之1+99*100分之1的和1/2+2/3+3/4+…+99/100=(1-1/2)+(
=(1-1/2)+(1-1/3)+(1-1/4)+…+(1-1/100)
=1*99-(1/2+1/3+…1/100)
=99+617/147
=7327/71
1*2分之1+2*3分之1+3*4分之1......98*99分之1+99*100分之1
=1/(1*2)+1/(2*3)+1/(3*4)........+1/(98*99)+1/(99*100)
=1-1/2+1/2-1/3+1/3-1/4+........+1/98-1/99+1/99-1/100
=1-1/100
=99/100