Bài giải:

$A=\left( 1-\frac{1}{4} \right)\times \left( 1-\frac{1}{9} \right)\times \left( 1-\frac{1}{16} \right)\times \left( 1-\frac{1}{25} \right)\times ...\times \left( 1-\frac{1}{121} \right)\times \left( 1-\frac{1}{144} \right)\times \left( 1-\frac{1}{169} \right)$

$=\frac{3}{4}\times \frac{8}{9}\times \frac{15}{16}\times \frac{24}{25}\times ..\times \frac{120}{121}\times \frac{143}{144}\times \frac{168}{169}$

$=\frac{1\times 3}{2\times 2}\times \frac{2\times 4}{3\times 3}\times \frac{3\times 5}{5\times 5}\times ...\times \frac{10\times 12}{11\times 11}\times \frac{11\times 13}{12\times 12}\times \frac{12\times 14}{13\times 13}$

$=\frac{\left( 2\times 3\times 4\times 5\times ...\times 11\times 12 \right)\times \left( 3\times 4\times 5\times 6\times ...\times 14 \right)}{\left( 2\times 3\times 4\times 5\times ...\times 13 \right)\times \left( 2\times 3\times 4\times 5\times ...\times 13 \right)}$

$=\frac{1}{13}\times \frac{14}{2}$

$=\frac{7}{13}$