1/x(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+.+1/(x-19)(x-20)
=[1/(x-1)-1/x]+[1/(x-2)-1/(x-1)]+[1/(x-3)-1/(x-2)]+.+[1/(x-20) -1/(x-19) ]
=1/(x-20)-1/x