Question

1/10+ 1/15 + 1/21 +.........+1/66

Answer 1

\(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+........+\frac{1}{66}\)

=\(\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...........+\frac{2}{132}\)

=\(2\left(\frac{1}{4.5}+\frac{1}{5.6}+..........+\frac{1}{11.12}\right)\)

=\(2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+..........+\frac{1}{11}-\frac{1}{12}\right)\)

=\(2\left(\frac{1}{4}-\frac{1}{12}\right)\)

=\(2.\frac{1}{6}\)

=\(\frac{1}{3}\)