1/a(a+1) + 1/(a+1)(a+2) + 1/(a+2)(a+3).1/(a+2003)(a+2004) =1/a-1/(a+1)+1/(a+1)-1/(a+2)+1/(a+2)-1/(a+3).+1/(a+2003)-1/(a+2004) =1/a-1/(a+2004) =2004/a(a+2004) ...