A=1/2-1/2^2+1/2^3-1/2^4+.......+1/2^99-1/2^100

Đáp án + Giải thích các bước giải:

Ta có:

`A = 1/2 - 1/2^2 + 1/2^3 - 1/2^4 +...+ 1/2^99 - 1/2^100`

`=> 2A = 1 - 1/2 + 1/2^2 - 1/2^3 +...+ 1/2^98 - 1/2^99`

`=> 2A + A = (1 - 1/2 + 1/2^2 - 1/2^3 +...+ 1/2^98 - 1/2^99) + (1/2 - 1/2^2 + 1/2^3 - 1/2^4 +...+ 1/2^99 - 1/2^100)`

`=> 3A = 1 - 1/2 + 1/2^2 - 1/2^3 +...+ 1/2^98 - 1/2^99 + 1/2 - 1/2^2 + 1/2^3 - 1/2^4 +...+ 1/2^99 - 1/2^100`

`=> 3A = 1 - 1/2^100`

`=> A = (1 - 1/2^100)/3`

Vậy `A = (1 - 1/2^100)/3`

$\textit{#toiyeubongda}$