7/6+13/12+21/20+31/30+…+421/420

7/6+13/12+21/20+31/30+…+421/420


原式= 1 + 1/(2*3)+ 1 +1/(3*4)+ 1 +1/(4*5)+ .+ 1 +1/(20*21)
=19 +(1/2 -1/3)+(1/3 -1/4)+(1/4 -1/5)+ .+(1/20 -1/21)
= 19 + 1/2 -1/21
=19又19/42