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