1x1/2+1/2x1/3+1/3x1/4+......+1/19x1/20=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/19-1/20)=1-1/2+1/2-1/3+1/3-1/4+...+1/19-1/20=1-1/20=19/20
