\(F=\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{190}\)
\(\Rightarrow F=\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+...+\frac{2}{380}\)
\(\Rightarrow F=\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+...+\frac{2}{19.20}\)
\(\Rightarrow F=2.\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{19}-\frac{1}{20}\right)\)
\(\Rightarrow F=2.\left(\frac{1}{5}-\frac{1}{20}\right)\)
\(\Rightarrow F=2.\frac{3}{20}\)
\(\Rightarrow F=\frac{3}{10}\)