2005×（1/1×2+1/2×3+1/3×4+…+1/2003×2004+1/2004×2005）
=2005×[(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2004-1/2005)]
=2005×(1-1/2005)
=2005-1
=2004