2分之1+6分之5+12分子11+20分之19+30分之29+..+9702分之9701+9900分之9899 简算

=(1-1/(1*2))+(1-1/(2*3))+(1-1/(3*4))+...+(1-1/(99*100))
=(1+1+1+...+1)-(1/(1*2)+1/(2*3)+(1/(3*4)+...+1/(99*100))
=100-((1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/99-1/100))
=100-(1/1-1/100)
=100-1+1/100=99+1/100=9901/100