A=\(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{15}+...+\dfrac{1}{380}\)
=\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{3.5}+.....+\dfrac{1}{19.20}\)
=\(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{3}-\dfrac{1}{5}+....+\dfrac{1}{19}-\dfrac{1}{20}\)
=\(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{20}=\dfrac{30}{60}-\dfrac{20}{60}-\dfrac{3}{60}=\dfrac{7}{60}\)