\(\frac{1}{3}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
= \(\frac{1}{3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{6.7}\)
= \(\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{6}-\frac{1}{7}\)
= \(\frac{1}{3}+\frac{1}{3}-\frac{1}{7}\)
= \(\frac{11}{21}\)