分式的加减.已知1/m-1/(m+1)=1/m(m+1),请你化简.

1/(n+1)(n+2)+1/(n+2)(n+3)+…+1/(n+2006)(n+2007)+1/(n+2007)(n+2008).
=1/(n+1)-1/(n+2)+1/(n+2)-1/(n+3)+…+1/(n+2006)-1/(n+2007)+1/(n+2007)-1/(n+2008).
=1/(n+1)-1/(n+2008).
=2007/[(n+1)(n+2008)]