Question

Answer 1

`@` `\text {Ans}`

`\downarrow`

`c)`

`8/9 - 1/72 - 1/56 - 1/42 - ... - 1/6 - 1/2`

`= 8/9 - (1/2 + 1/6 + ... + 1/42 + 1/56 + 1/72)`

`= 8/9 - `\(\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}\right)\)

`=`\(\dfrac{8}{9}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{8}-\dfrac{1}{9}\right)\)

`= 8/9 - (1 - 1/9)`

`= 8/9 - 8/9`

`= 0`