1乘3分之1加2乘4分之1……19×21分之一等于什么

1/(1*3)+1/(2*4)+1/(3*5)+…+1/(18*20)+1/(19*21)
=1/2[(1/1-1/3)+(1/2-1/4)+(1/3-1/5)+…+(1/18-1/20)+(1/19-1/21)]
=1/2(1 + 1/2- 1/20 - 1/21)
=589/840