Tính C = \(\left( {1 - \frac{1}{4}} \right)\left( {1 - \frac{1}{9}} \right)\left( {1 - \frac{1}{{16}}} \right)....\left( {1 - \frac{1}{{100}}} \right)\).

C = \(\left( {1 - \frac{1}{4}} \right)\left( {1 - \frac{1}{9}} \right)\left( {1 - \frac{1}{{16}}} \right)....\left( {1 - \frac{1}{{100}}} \right)\)

C = \(\frac{3}{4}.\frac{8}{9}.\frac{{15}}{{16}}...\frac{{99}}{{100}}\)

C = \(\frac{{1.3}}{{2.2}}.\frac{{2.4}}{{3.3}}......\frac{{9.11}}{{10.10}}\)

C = \(\frac{{1.3.2.4.3.5....9.11}}{{2.2.3.3.4.4....10.10}}\)

C = \(\frac{{1.2.3.4....9}}{{2.3.4.5....10}}.\frac{{3.4.5.6....11}}{{2.3.4.5....10}}\)

C = \(\frac{1}{{10}}.\frac{{11}}{2}\)

C= \(\frac{{11}}{{20}}\).