1/x(x+2)+1/(x+2)*(x+4)+1/(x+4)*(x+6)+.+1/(x+2000)*(x+2002)=1/2(1/x-1/(x+2))+1/2(1/(x+2)-1/(x+4))+1/2(1/(x+4)-1/(x+6))+.+1/2(1/(x+2000)-1/(x+2002))=1/2(1/x-1/(x+2002))=1/2(2002/x(x+2002))=1001/x(x+2002...