解;【1/3-1/2】+【1/4-1/3】+【1/5-1/4】+……+【1/2004-1/2003】
=-[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/2003-1/2004)]
=-[1/2-1/3+1/3-1/4+1/4-1/5+……+1/2003-1/2004]
=-(1/2-1/2004）=-1001/2004