1/20+1/30+1/42+.....+1/240
=1/4.5+1/5.6+1/6.7+.....+1/15.16
=1/4-1/5+1/5-1/6+1/6-1/7+......+1/15-1/16
=1/4-1/16
=4/16-1/16
=3/16
\(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\)
=\(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\)
=\(\frac{1}{4}-\frac{1}{16}\)
=\(\frac{3}{16}\)