1/(a-1)（a-2)+1/(a-2)(a-3)+1(a-3)(a-4)+.+1(a-9)(a-10)
=1/(a-2)-1/(a-1)+1/(a-3)-1/(a-2)+.1/(a-10)-1/(a-9)
=1/(a-10)-1/(a-1)
=9/(a-10)(a-1)