Question

1/6+1/12+1/20+1/30+1/42...+1/240

Answer 1

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{240}\)

= \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{15.16}\)

= \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{15}-\frac{1}{16}\)

= \(\frac{1}{2}-\frac{1}{16}\)

= \(\frac{7}{16}\)