\(\left(1-\frac{1}{49}\right)\left(1-\frac{1}{64}\right)\left(1-\frac{1}{81}\right)\left(1-\frac{1}{100}\right)\left(1-\frac{1}{21}\right)\left(1-\frac{1}{144}\right)\)
\(=\frac{48}{49}.\frac{63}{64}.\frac{80}{81}.\frac{99}{100}.\frac{120}{121}.\frac{144}{143}\)
\(=\frac{48.63.80.99.120.143}{49.64.81.100.121.144}\)
\(=\frac{6.8.7.9.8.10.11.9.20.6.13.11}{7.7.8.8.9.9.10.10.11.11.6.2.6.2}\)
\(=\frac{13}{14}\)