1/x(x+2)+1/(x+1)(x+3)+1/(x+2)(x+4).+1/(x+2007)(x+2009)=1/2[2/x(x+2)+2/(x+1)(x+3)+2/(x+2)(x+4).+2/(x+2007)(x+2009)]=1/2[1/x-1/(x+2)+1/(x+1)-1/(x+3)+1/(x+2)-1/(x+4).+1/(x+2007)-1/(x+2009)]=1/2[1/x+1/(x+...