Question

(1-1/2)(1-1/3)....(1-1/199)(1-1/200)

Answer 1

\(=\left(\dfrac{2}{2}-\dfrac{1}{2}\right)\left(\dfrac{3}{3}-\dfrac{1}{3}\right)...\left(\dfrac{199}{199}-\dfrac{1}{199}\right)\left(\dfrac{200}{200}-\dfrac{1}{200}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{198}{199}\cdot\dfrac{199}{200}=\dfrac{1}{200}\)

Answer 2

`(1 - 1/2)(1 - 1/3) ... (1 - 1/199)(1 - 1/200)`

`= 1/2 . 2/3 ... 198/199 . 199/200`

`= 1/101 + 1/102 + ... + 1/200` (`dpcm`)