A= 1/2 + 1/4+ 1/8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 (1) 

=> 2A=1+ 1/2 + 1/4+ 1/8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256 (2) 

Lấy (1)-(2) 
=> 2A-A=(1+ 1/2 + 1/4+ 1/8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256)-(1/2 + 1/4+ 1/8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512) 

=>A=1-1/512=511/512 

5* nha bạn

cảm ơn bạn nhiều nha.Mình rồi đó

x : 1/2 + x : 1/4 + x : 1/8 + ... + x : 1/512 = 511

=> x . 2 + x . 4 + x . 8 + ... + x . 512 = 511

=> x . 2 + x . 2² + x . 2³ + ... + x . 2⁹ = 511

=> x . (2 + 2² + 2³ + ... + 2⁹) = 511

=> x . 1022 = 511

=> x = 511 : 1022

=> x = 1/2 (Loại)

Vậy x thuộc rỗng.

Tính sai rồi bạn ơi 2+2^2+2^3+.....+2^9 ko phải bằng 1022

1022 đúng rồi mà

\(x:\frac{1}{2}+x:\frac{1}{4}+x:\frac{1}{8}+..+x:\frac{1}{512}=x.2+x.4+x.8+...x.512=x\left(2+4+8+...+512\right)=...\)

\(x:\dfrac{1}{2}+x:\dfrac{1}{4}+x:\dfrac{1}{8}+...+x:\dfrac{1}{512}=511\\ 2x+4x+8x+..+512x=511\\ x\left(2+4+8+...+512\right)=511\\ x\left(2^1+2^2+2^3+...+2^9\right)=511\\ \)

Gọi \(S=2^1+2^2+2^3+...+2^9\)

\(2S=2^2+2^3+2^4+...+2^{10}\\ 2S-S=\left(2^2+2^3+2^4+...+2^{10}\right)-\left(2^1+2^2+2^3+...+2^9\right)\\ S=2^{10}-2\)

\(x\left(2^{10}-2\right)=511\\ 2x\left(2^9-1\right)=511\\ 2x\left(512-1\right)=511\\ 2x\cdot511=511\\ 2x=1\\ x=\dfrac{1}{2}\)

Vậy \(x=\dfrac{1}{2}\)