\(S=\frac{1.4}{3.7.4}+\frac{1.4}{7.11.4}+......+\frac{1.4}{19.23.4}\)

    \(=\frac{1}{4}.\left(\frac{4}{3.7}+\frac{4}{7.11}+......+\frac{4}{19.23}\right)\)

    \(=\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+......+\frac{1}{19}-\frac{1}{23}\right)\)

   \(=\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{23}\right)\)

   \(=\frac{1}{4}.\frac{20}{69}=\frac{5}{69}\)