Bài giải:

$A=\left( 1+\frac{7}{9} \right)\times \left( 1+\frac{7}{20} \right)\times \left( 1+\frac{7}{33} \right)\times ...\times \left( 1+\frac{7}{2900} \right)$

$=\frac{16}{9}\times \frac{27}{20}\times \frac{40}{33}\times ...\times \frac{2907}{2900}$

$=\frac{2\times 8}{1\times 9}\times \frac{3\times 9}{2\times 10}\times \frac{4\times 10}{3\times 11}\times ...\times \frac{51\times 57}{50\times 58}$

$=\frac{\left( 2\times 3\times 4\times ...\times 51 \right)\times \left( 8\times 9\times 10\times ...\times 57 \right)}{\left( 1\times 2\times 3\times ...\times 50 \right)\times \left( 9\times 10\times 11\times ...\times 58 \right)}$

$=\frac{51}{1}\times \frac{8}{58}$

$=\frac{204}{29}$