1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+2013)(x+2014)=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+.+1/(x+2013)-1/(x+2014)=1/x-1/(x+2014)=2014/x(x+2014)