Question

Simplify: `(1 - 1/2)(1 - 1/3) ......... (1 - 1/9)(1 - 1/10)`

विकल्प

• `- 1/10`

• `5/6`

• 0

• `1/10`

Answer 1

`1/10`

Explanation:

Given, `(1 - 1/2)(1 - 1/3) ....... (1 - 1/9)(1 - 1/10)`

= `(1 - 1/2)(1 - 1/3)(1 - 1/4) ....... (1 - 1/9)(1 - 1/10)`

= `((2 - 1)/2)((3 - 1)/3)((4 - 1)/4) ....... ((8 - 1)/8)((9 - 1)/9)((10 - 1)/10)`

= `1/2 xx 2/3 xx 3/4 xx .............. xx 7/8 xx 8/9 xx 9/10`

= `1 xx 1/10`

= `1/10`