2+4+6+……+2n=n(n+1)
所以原式=1/1*2+1/2*3+1/3*4+……+1/1002*1003
=1-1/2+1/2-1/3+1/3-1/4+……+1/1002-1/1003
=1-1/1003
=1002/1003