\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}...\frac{30}{62}.\frac{31}{64}\)
\(=\frac{1.2.3.4...30.31}{2.2.2.3.2.4.2.5...2.31.2.32}\)
\(=\frac{1.2.3.4...30.31}{2^{31}.\left(2.3.4.5...31\right).32}\)
\(=\frac{1}{2^{31}.32}\)
\(=\frac{1}{2^{31}.2^5}\)
\(=\frac{1}{2^{36}}\)