$\iff 10A=\genfrac{}{}{0ex}{}{10\left(10^{2004}+1\right)}{10^{2005}+1}$

$\Rightarrow 10A=\genfrac{}{}{0ex}{}{10^{2005}+10}{10^{2005}+1}$

$10A=\genfrac{}{}{0ex}{}{10^{2005}+1+9}{10^{2005}+1}=\genfrac{}{}{0ex}{}{10^{2005}+1}{10^{2005}+1}+\genfrac{}{}{0ex}{}{9}{10^{2005}+1}$

$10A=1+\genfrac{}{}{0ex}{}{9}{10^{2005}+1}$

tương tự như trên ta có :

$10B=1+\genfrac{}{}{0ex}{}{9}{10^{2006}+1}$

ta thấy:102005+1<102006+1

$\Rightarrow \genfrac{}{}{0ex}{}{9}{10^{2005}+1}>\genfrac{}{}{0ex}{}{9}{10^{2006}+1}$

$\Rightarrow 1+\genfrac{}{}{0ex}{}{9}{10^{2005}+1}>1+\genfrac{}{}{0ex}{}{9}{10^{2006}+1}$

=>10A>10B

=>A>B