7/6+13/12+21/20+31/30+.421/420

7/6+13/12+21/20+31/30+。421/420=1+1/6+1+1/12+1+1/20+。。。+1+1/420=19×1+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+。。。+(1/20-1/21)=19+1/2-1/3+1/3-1/4+1/4-1/5+。。。+1/20-1/21=19+1/2-1/21=19+21/42-2/42=19又42分之19；如果本题有什么不明白可以追问,