Question

Giúp e với ạ

Answer 1

`A = 0,2+ (0,2)^2 + (0,2)^3 + ... + (0,2)^100`

`A = 1/5  + (1/5)^2 + (1/5)^3 + ... + (1/5)^100`

`5A = 5 . [1/5  + (1/5)^2 + (1/5)^3  ... + (1/5)^100]`

`5A = 1 + 1/5 + (1/5)^2 + ...+ (1/5)^99`

`5A - A = [1 + 1/5 + (1/5)^2 + ... + (1/5)^99]-[1/5  + (1/5)^2 + (1/5)^3 + ... + (1/5)^100]`

`4A = 1 - (1/5)^100`

`A = (1-(1/5)^100)/4`

Vì: `1 - (1/5)^100 < 1` hay `(1-(1/5)^100)/4 < 1/4` nên `A < 1/4`

Vậy: `A <1/4`

Answer 2

`A = 0,2 + (0,2)^2 + ... +(0,2)^100 `

`=> 0,2A = (0,2)^2 + ... + (0,2)^101`

`=> 0,2A - A = ((0,2)^2 + ... + (0,2)^101) -(0,2 + ... +(0,2)^100) `

`=> -0,8A = (0,2)^101 - 0,2`

`=> A = -0,8*((0,2)^101 - 0,2)`

Vì `(0,2)^101 - 0,2>0`

`=> -0,8*((0,2)^101 - 0,2)<0`

Mà `1/4 >0`

`=>  -0,8*((0,2)^101 - 0,2)<1/4`

`=> A<1/4`