1/1*3+1/2*4+1/3*5+.+1/18*20
=1/2*(1-1/3)+1/2*(1/2-1/4)+1/2*(1/3-1/5)+.+1/2*(1/17-1/19)+1/2*(1/18-1/20)
=1/2*(1-1/3+1/3-1/5+.+1/17-1/19)+1/2*(1/2-1/4+1/4-1/6+.+1/18-1/20)
=1/2*(1-1/19)+1/2*(1/2-1/20)
=1/2*18/19+1/2*(10/20-1/20)
=9/19+9/20*1/2
=9/19+9/40
=360/760+171/760
=531/760