(1/2+1/3.......+1/2003)×(1+1/2+1/3.......+1/2004)-(1+1/2+1/3.......+1/2003)×(1/2+1/3.......+1/2004)= (1/2+1/3.......+1/2003)×[(1+1/2+1/3.......+1/2003)+1/2004]-(1+1/2+1/3.......+1/2003)×[(1/2+1/3.......+1/2003)+1/2004]= (1/2+1/3.......+1/2003)×(1+1/2+1/3.......+1/2003)+(1/2+1/3.......+1/2003)×1/2004-(1+1/2+1/3.......+1/2003)×(1/2+1/3.......+1/2003)-(1+1/2+1/3.......+1/2003)×1/2004=(1/2+1/3.......+1/2003)×1/2004-(1+1/2+1/3.......+1/2003)×1/2004=(1/2+1/3.......+1/2003)×1/2004-(1/2+1/3.......+1/2003)×1/2004-1×1/2004=-1/2004