\(\left(1-\frac{3}{4}\right).\left(1-\frac{3}{7}\right).\left(1-\frac{3}{10}\right).\left(1-\frac{3}{13}\right)...\left(1-\frac{3}{97}\right).\left(1-\frac{3}{100}\right)\)
\(=\frac{1}{4}.\frac{4}{7}.\frac{7}{10}.\frac{10}{13}...\frac{94}{97}.\frac{97}{100}\)
\(=\frac{1.4.7.10...94.97}{4.7.10.13...97.100}=\frac{1}{100}.\)