2分之3+6分之7+12分之13+20分之21……420分之421
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+.+(1/20-1/21)+1×20
=1-1/21 + 20
=20又 20/21