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,