\(A=\dfrac{1}{3}\left(1+\dfrac{1}{2}+...+\dfrac{1}{256}+\dfrac{1}{512}\right)\)

Đặt B=1+1/2+...+1/256+1/512

=>2B=2+1+...+1/128+1/256

=>B=2-1/512=1023/512

=>\(A=\dfrac{1}{3}\cdot\dfrac{1023}{512}=\dfrac{341}{512}\)

\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}+\frac{1}{384}+\frac{1}{768}+\frac{1}{1536}\)

\(A\times2=\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{96}+\frac{2}{192}+\frac{2}{384}+\frac{2}{768}+\frac{2}{1536}\)

Rút gọn ta được

\(A\times2=\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}+\frac{1}{384}+\frac{1}{768}\)

\(A\times2-A=\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{768}-\left[\frac{1}{3}+\frac{1}{6}+...+\frac{1}{1536}\right]\)

\(A=\frac{2}{3}+\frac{1}{3}-\frac{1}{3}-\frac{1}{1536}\)

\(A=\frac{2}{3}-\frac{1}{1536}=\frac{341}{512}\)

Bạn hiểu cách làm lớp 6 ko mk gửi

X*3069=3069

X=3069/3069

X-1

X = 3069/3069

X = 1

k cho minh nha

Gọi tổng đó là A

A = 1/6+1/12+1/24+...+1/768

A x 2 = 1/3 + 1/6 + 1/12 + 1/24 + .... + 1/384

A x 2 - A = 1/3 + 1/6 + 1/12 + 1/24 + .... + 1/384 -  1/6 + 1/12 + 1/24 + ... + 1/768

A = 1/3 - 1/768 = 85/256

Gọi tổng đó là Z

Z = 1/6+1/12+1/24+...+1/768

Z . 2 = 1/3 + 1/6 + 1/12 + 1/24 + .... + 1/384

Z . 2 - A = 1/3 + 1/6 + 1/12 + 1/24 + .... + 1/384 -  1/6 + 1/12 + 1/24 + ... + 1/768

Z = 1/3 - 1/768 = 85/256