Question

\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\)

Answer 1

`= 1/(1.2) + 1/(2.3) + ... + 1/(9.10)`

`= 1/1 - 1/2 + 1/2 - 1/3 + ... + 1/9 - 1/10`

`= 9/10`

Answer 2

\(=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+....+\dfrac{1}{9.10}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+..+\dfrac{1}{9}-\dfrac{1}{10}\)

\(=1-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{10}\)

\(=\dfrac{17}{20}\)

Answer 3

\(=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+...+\dfrac{1}{9.10}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\)

\(=1-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{10}\)

\(=\dfrac{17}{20}\)