A = $\frac{2003}{2004}$ + $\frac{2004}{2005}$ + $\frac{2005}{2003}$
= 1 - $\frac{1}{2004}$ + 1 - $\frac{1}{2005}$ + 1 + $\frac{1}{2003}$ + $\frac{1}{2003}$
= (1 + 1 + 1) + ($\frac{1}{2003}$ - $\frac{1}{2004}$) + ($\frac{1}{2003}$ - $\frac{1}{2005}$)
= 3 + ($\frac{1}{2003}$ - $\frac{1}{2004}$) + ($\frac{1}{2003}$ - $\frac{1}{2005}$) > 3
Vậy A > 3