Question

1/(x-1)+1/(x-1)(x-2)+...+1/(x-2010)(x-2011)

Answer 1

利用：1/(x-(n+1))- 1/(x-n)=1/(x-n)(x-(n+1)) 来解

如：1/(x-2)- 1/(x-1)=1/(x-1)(x-2)

所以：1/(x-1)+1/(x-1)(x-2)+...+1/(x-2010)(x-2011)

=1/(x-1)+ 1/(x-2)- 1/(x-1)+……+1/(x-2011)- 1/(x-2010)

=1/(x-2011)