\(\dfrac{x}{1024}=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+...-\dfrac{1}{1024}\)

\(\dfrac{2x}{1024}=1-\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{8}+...-\dfrac{1}{512}\)

\(\Rightarrow\dfrac{x}{1024}+\dfrac{2x}{1024}=1-\dfrac{1}{1024}\)

\(\Rightarrow\dfrac{3x}{1024}=\dfrac{1023}{1024}\)

\(\Rightarrow3x=1023\)

\(\Rightarrow x=341\)

Lời giải:

$\frac{x}{1024}=\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+...-\frac{1}{1024}$

$\frac{2x}{1024}=1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+...-\frac{512}$

$\Rightarrow \frac{x}{1024}+\frac{2x}{1024}=1-\frac{1}{1024}$

$\frac{3x}{1024}=\frac{1023}{1024}$

$\Rightarrow 3x=1023$

$\Rightarrow x=341$

A = 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/512 + 1/1024

A x 2 = 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/512

A x 2 - A = 1 + 1/2 - 1/2+ 1/4 -1/4 + 1/8 -1/8 + 1/16 -1/16 + ... + 1/512 - 1/512 - 1/1024

A = 1 - 1/1024

A = 1023/1024

la 1023/1024 ban nha

A = 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/512 + 1/1024

A x 2 = 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/512

A x 2 - A = 1 + 1/2 - 1/2+ 1/4 -1/4 + 1/8 -1/8 + 1/16 -1/16 + ... + 1/512 - 1/512 - 1/1024

A = 1 - 1/1024

A = 1023/1024

kết quả là 1/1024

lớp 1 kinh thế. lớp 6 chứ

chuyển thành công đi cho dẽ nhìn

A=1-(1/2+1/4+1/8+1/16...+1/1024)

B=(1-A)=1/2+1/4+1/8+...+1/1024

B=1/2+1/2^2+1/2^3+..+1/2^10  (cái này có công thức cấp số nhân) 

có thể chưa học cách làm bình thừng như sau

1/2.B=1/2^2+1/2^3+...+1/2^10+1/2^11

Trừ cho nhau

1/2B=1/2 -1/2^11 ( cái giữa triệt tiêu)

B=1-1/2^10

A=1-B=1/2^10

DS: 1/2^10

gọi A=1/2+1/4+1/8+...+1/1024

2xA=1+1/2+1/4+.....+1/512

2xA-A=(1+1/2+1/4+....+1/512)-(1/2+1/4+1/8+...+1/1024)

A=1-1/1024

=1023/1024

vậy A=1023/1024

A=\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\)

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{512}-\frac{1}{1024}\)

=1-1/1024

=1023/1024

A = 1/2+1/4+...+1/2048

2A= 1+ 1/2+ 1/4+...+1/1024

2A-A= ( 1+ 1/2+...+1/1024 ) -  (1/2+1/4+...+2048)

A= 1- 1/2048

A= 2047/2048

2047/1024

\(\frac{2047}{1024}\)

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