Question

1/2+1/6+1/12+1/20+1/30+1/42 =?

Answer 1

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{42}=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{6\times7}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{6}-\frac{1}{7}=1-\frac{1}{7}=\frac{6}{7}\)

Answer 2

\(\frac{1}{2} +\frac{1}{6}+\frac{1}{21}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}=\frac{23}{28}\)

Answer 3

= 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6,7

= 1 - 1/2  +1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/4 + 1/5 - 1/6 + 1/6 - 1/7

= 1 - 1/7

= 6/7