1/a（a+1）=1/a-1/(a+1)
所以1/a（a+1）+1/(a+1)(a+2)+...+1/(a+2007)(a+2008)=1/a-1/(a+1)+1/(a+1)-1/(a+2)+...+1/(a+2007)-1/(a+2008)中间项消掉了
=1/a-1/(a+2008)=2008/a(a+2008)