1-1/1*2-2-1/2*3-1/3*4-1/4*5-……1/2003*2004
=1-(1-1/2)-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)……-（1/2003-1/2004)
=1-1+1/2-1/2+1/3-1/3……-1/2003+1/2004
=1/2004