ab分之1+（a+1）（b+1）分之1+.（a+2004）（b+2004）分之1
=1/1×2+1/2×3+1/3×4+……+1/2005×2006
=1-1/2+1/2-1/3+1/3-1/4+……+1/2005-1/2006
=1-1/2006
=2005/2006