Bài giải:

$A=\left( 1+\frac{2}{1\times 4} \right)\times \left( 1+\frac{2}{2\times 5} \right)\times \left( 1+\frac{2}{3\times 6} \right)\times ...\times \left( 1+\frac{2}{50\times 53} \right)$

$A=\frac{2\times 3}{1\times 4}\times \frac{3\times 4}{2\times 5}\times \frac{4\times 5}{3\times 6}\times ...\times \frac{51\times 52}{50\times 53}$

$A=\frac{\left( 2\times 3\times 4\times ...\times 51 \right)\times \left( 3\times 4\times 5\times ...\times 52 \right)}{(1\times 2\times 3\times ...\times 50)\times \left( 4\times 5\times 6\times ...\times 53 \right)}$

$A=\frac{51}{1}\times \frac{3}{53}=\frac{153}{53}$