1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3 )+……+1/(a+2009)(a+2010)=1/a-1/(a+1)+1/(a+1)-1/(a+2)+1/(a+2)-1/(a+3 )+……+1/(a+2009)-1/(a+2010)=1/a-1/(a+2010)=2010/[a(a+2010)]