Bài giải:

$A=\left( 1-\frac{1}{3} \right)\times \left( 1-\frac{1}{6} \right)\times \left( 1-\frac{1}{10} \right)\times \left( 1-\frac{1}{15} \right)\times ...\times \left( 1-\frac{1}{36} \right)$

$A=\frac{2}{3}\times \frac{5}{6}\times \frac{9}{10}\times \frac{14}{15}\times ...\times \frac{35}{36}$

$A=\frac{4}{6}\times \frac{10}{12}\times \frac{18}{20}\times \frac{28}{30}\times ...\times \frac{70}{72}$

$A=\frac{1\times 4}{2\times 3}\times \frac{2\times 5}{3\times 4}\times \frac{3\times 6}{4\times 5}\times \frac{4\times 7}{5\times 6}\times ...\times \frac{7\times 10}{8\times 9}$

$A=\frac{\left( 1\times 2\times 3\times 4\times ...\times 7 \right)\times \left( 4\times 5\times 6\times 7\times ...\times 10 \right)}{\left( 2\times 3\times 4\times 5\times ...\times 8 \right)\times \left( 3\times 4\times 5\times 6\times ...\times 9 \right)}$

$A=\frac{1}{8}\times \frac{10}{3}=\frac{5}{12}$