A=1/2+1/6+1/12+1/24+…+1/192+1/384

Giải

Ta có:

A x 2 =(1/2+1/6+1/12+1/24+…+1/192+1/384) x 2

A x 2 = 1 + 2/6 + 2/12 + 2/24 + ... + 2/192 + 2/384

Rút gọn ta được:

A x 2 = 1 + 1/3 + 1/6 + 1/12 + ... + 1/96 + 1/192

A x 2 - A = 1 + 1/3 + 1/6 + 1/12 + ... + 1/96 + 1/192 - (1/2+1/6+1/12+1/24+…+1/192+1/384)

A = 1 + 1/3 - 1/2 - 1/384

A = 5/6 - 1/384

A = 319/384

ĐS: 319/384

Sao đề bài là 1/3 còn khi làm là1/2 hả

1/3 + 1/6 + 1/12 + 1/24 + 1/48 + 1/96 + 1/192

= 127/192

k minh di , xin day

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

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

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

Đáp số: 341/512

A = 1/3 + 1/6 + 1/12 + 1/24 + 1/48 + 1/96 + 1/192

A x 2 = 2/3 - ( 1/3 + 1/6 + 1/12 + 1/24 +1/48 + 1/96 + 1/192 ) - 1/192

A x 2 = 2/3 - A - 1/92

A x 2 - A = 2/3 - 1/92

A           = bạn tự tính nha mk đang vợi bạn thông cảm cho

1/3 + 1/6+1/12+1/24+1/48+1/96
= 2/3 – 1/3 + 1/3 – 1/6+1/6- 1/12+1/12- 1/24+1/24-1/48+1/48-1/96
=2/3_1/96

= 63/99
= 21/32

= 2x(1/3+1/6+1/12+1/24+1/48+1/96+1/192)

= 2x(1-1/3+1/3-1/6+1/6-1/12+1/12-1/24+1/24-1/48+1/48-1/96+1/96-1/192)

= 2x(1-1/192)

= 2x191/192

=382/192=191/96

1/3 + 1/6 + 1/12 + 1/24 + 1/48 + 1/96 + 1/192 + 1/384 = 85/128

0.6640625

85/128 nha 

\(=2\left(\frac{1}{3}+\frac{1}{6}+...+\frac{1}{192}\right)\)

\(=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{6}+...+\frac{1}{96}-\frac{1}{192}\right)\)

\(=2\left(1-\frac{1}{192}\right)\)

\(=2\times\frac{191}{192}\)

\(=\frac{191}{96}\)