Đáp án:

Giải thích các bước giải:

 `A=-3/(2^2)-3/(2^3)-3/(2^4)+....-3/(2^100)`
`<=>2A=-3/2-3/(2^2)-3/(2^3)-...-3/(2^99)`
`=>2A-A = -3/2-3/2^2-3/2^3-...-3/2^99 -( -3/(2^2)-3/(2^3)-3/(2^4)+....-3/(2^100))`
`<=>A=-3/2+3/2^100`
Vậy`A=-3/2+3/2^100`

 `A=(-3/2)^2+(-3/2)^3+(-3/2)^4+....+(-3/2)^100`

 `<=>A=9/(2^2)+9/(2^3)+9/(2^4)+....+9/(2^100)`

`=> 2A =9/2+9/(2^2)+9/(2^3)+...+9/(2^99)`

`<=> 2A-A= (9/2+9/(2^2)+9/(2^3)+...+9/(2^99))- (9/(2^2)+9/(2^3)+9/(2^4)+....+9/(2^100))`

`<=> A=9/2-9/(2^100)`

Vậy ` A=9/2-9/(2^100)`