Bài giải:

$A=\left( \frac{6}{8}+1 \right)\times \left( \frac{6}{18}+1 \right)\times \left( \frac{6}{30}+1 \right)\times ...\times \left( \frac{6}{10700}+1 \right)$

$=\frac{14}{8}\times \frac{24}{18}\times \frac{36}{30}\times ...\times \frac{10706}{10700}$

$=\frac{2\times 7}{1\times 8}\times \frac{3\times 8}{2\times 9}\times \frac{4\times 9}{3\times 10}\times ...\times \frac{101\times 106}{100\times 107}$

$=\frac{\left( 2\times 3\times 4\times ...\times 101 \right)\times \left( 7\times 8\times 9\times ...\times 106 \right)}{\left( 1\times 2\times 3\times ...\times 100 \right)\times \left( 8\times 9\times 10\times ...\times 107 \right)}$

$=\frac{101}{1}\times \frac{7}{107}$

$=\frac{707}{107}$