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

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

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

a: \(A=1+\frac15+\frac{1}{25}+\cdots+\frac{1}{78125}\)

=>\(A=1+\frac15+\frac{1}{5^2}+\cdots+\frac{1}{5^7}\)

=>\(5\times A=5+1+\frac15+\cdots+\frac{1}{5^6}\)

=>\(5\times A-A=5+1+\frac15+\cdots+\frac{1}{5^6}-1-\frac15-\cdots-\frac{1}{5^7}\)

=>\(4\times A=5-\frac{1}{5^7}=\frac{5^8-1}{5^7}\)

=>\(A=\frac{5^8-1}{4\times5^7}\)

b:Sửa đề: \(B=\frac13+\frac{1}{12}+\cdots+\frac{1}{49152}\)

=>\(B=\frac13+\frac{1}{3\times4}+\frac{1}{3\times4^2}+\cdots+\frac{1}{3\times4^7}\)

=>\(4\times B=\frac43+\frac13+\frac{1}{3\times4}+\cdots+\frac{1}{3\times4^6}\)

=>\(4\times B-B=\frac43+\frac13+\frac{1}{3\times4}+\cdots+\frac{1}{3\times4^6}-\frac13-\frac{1}{3\times4}-\frac{1}{3\times4^2}-\cdots-\frac{1}{3\times4^7}\)

=>\(3\times B=\frac43-\frac{1}{3\times4^7}=\frac{4^8-1}{3\times4^7}\)

=>\(B=\frac{4^8-1}{9\times4^7}\)

c: \(C=\frac53+\frac56+\frac{5}{12}+\frac{5}{24}+\cdots+\frac{5}{192}+\frac{5}{384}\)

=>\(2\times C=\frac{10}{3}+\frac53+\frac56+\cdots+\frac{5}{96}+\frac{5}{192}\)

=>\(2\times C-C=\frac{10}{3}+\frac53+\frac56+\cdots+\frac{5}{96}+\frac{5}{192}-\frac53-\frac56-\cdots-\frac{5}{192}-\frac{5}{384}\)

=>\(C=\frac{10}{3}-\frac{5}{384}=\frac{1280}{384}-\frac{5}{384}=\frac{1275}{384}\)

0.6640625

85/128 nha 

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

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

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

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

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