\(S=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{37.39}\)
=> \(S=\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{37.39}\right)\)
=> \(S=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{37}-\frac{1}{39}\right)\)
=> \(S=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{39}\right)=\frac{2}{13}\).