\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+......+\frac{1}{380}\)
=\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...............+\frac{1}{19.20}\)
=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+..............+\frac{1}{19}-\frac{1}{20}\)
=\(\frac{1}{2}-\frac{1}{20}\)
=\(\frac{9}{20}\)