1x3分之1+2x4分之1+3x5分之1+.+18x20分之1
=1/(1*3)+1/(2*4).+1/(18*20)
=[1/1-1/3]/2+[1/2-1/4]/2.+[1/18-1/20]/2
=1/2[(1/1+1/2+1/3+1/4...1/18)-(1/3+1/4+1/5+.+1/20)]
=1/2*[1/1+1/2-1/19-1/20]
=1/2*[18/19+9/20]
=531/[2*19*20]
=531/760