因为1/(x+n)(x+n+2)=1/2*[1/(x+n)-1/(x+n+2)]
所以原式=1/x-1/(x+2)+1/(x+2)-1/(x+4)+...+1/(x+2000)-1/(x+2002)
=1/x-1/(x+2002)
=2002/x(x+2002)