Bài giải:

$A=\left( \frac{28}{10}-1 \right)\times \left( \frac{52}{22}-1 \right)\times \left( \frac{80}{36}-1 \right)\times ...\times \left( \frac{21808}{10900}-1 \right)$

$A=\frac{18}{10}\times \frac{30}{22}\times \frac{44}{36}\times ...\times \frac{10908}{10900}$

$A=\frac{2\times 9}{1\times 10}\times \frac{3\times 10}{2\times 11}\times \frac{4\times 11}{3\times 12}\times ...\times \frac{101\times 108}{100\times 109}$

$A=\frac{\left( 2\times 3\times 4\times ...\times 101 \right)\times \left( 9\times 10\times 11\times ...\times 108 \right)}{\left( 1\times 2\times 3\times ...\times 100 \right)\times \left( 10\times 11\times 12\times ...\times 109 \right)}$

$A=\frac{101}{1}\times \frac{9}{109}=\frac{909}{109}$