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

ta có: A = 1/3 + 1/6 + 1/12 + 1/24 + ...+1/192 + 1/384

  = 1 - 1/3 + 1/3 - 1/6 + 1/6 - 1/12 + 1/12 + 1/24 + 1/24 -.......-  1/192 + 1/192 - 1/384 + 1/384

= 1 - 1/384

= 384/384 - 1/384

= 383/384

  nha

=1-1/384

=384/384-1/384

=383/384

=1-1/384

=384/384-1/384

=383/384

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

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

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

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 = \(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{192}+\frac{1}{384}\)

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 .

A = \(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+.......+\frac{1}{192}+\frac{1}{384}\)

A = \(\frac{1}{384}x128+\frac{1}{384}x64+\frac{1}{384}x32+.......+\frac{1}{384}x1\)

A = \(\frac{1}{384}x\left(128+64+32+16+8+4+2+1\right)\)

A = \(\frac{1}{384}x255\)

A = \(\frac{85}{128}\)

0.6640625

85/128 nha 

\(a,\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+....+\frac{1}{384}\)

\(\text{Đ}\text{ặt}\)\(A=\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{384}\)

\(2A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+....+\frac{1}{192}\)

\(2A-A=\frac{1}{3}-\frac{1}{384}\)

a đề sai

b)Đặt A=1/4x7 + 1/7x10 + 1/10x13 +...........+ 1/19x22

\(3A=3\left(\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{19.22}\right)\)

\(3A=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{19}-\frac{1}{22}\)

\(3A=\frac{1}{4}-\frac{1}{22}\)

\(A=\frac{9}{44}:3\)

\(A=\frac{3}{44}\)