∑(i=1,n)1/(x-i)(x-i-1)
=1/[(x-1)(x-2)]+1/[(x-2)(x-3)]+1/[(x-3)(x-4)]+.+1/[(x-i)(x-i-1)]
=1/(x-2)-1/(x-1)+1/(x-3)-1/(x-2)+.+1/(x-i-1)-1/(x-i)
=1/(x-i-1)-1/(x-1)
∑(i=1,n)1/(x-i)(x-i-1)
=1/[(x-1)(x-2)]+1/[(x-2)(x-3)]+1/[(x-3)(x-4)]+.+1/[(x-i)(x-i-1)]
=1/(x-2)-1/(x-1)+1/(x-3)-1/(x-2)+.+1/(x-i-1)-1/(x-i)
=1/(x-i-1)-1/(x-1)