\(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

\(=\frac{729}{729}+\frac{243}{729}+\frac{81}{729}+\frac{27}{729}+\frac{9}{729}+\frac{3}{729}+\frac{1}{729}\)

\(=\frac{729+243+81+27+9+3+1}{729}\)

\(=\frac{1087}{729}\)

Đặt \(A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

\(3A=3+1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)

\(3A-A=3-\frac{1}{729}\)nên \(2A=3-\frac{1}{729}\)

kHI ĐÓ \(A=\left(3-\frac{1}{729}\right):2=\frac{3}{2}-\frac{1}{1458}=\frac{2197}{1458}-\frac{1}{1458}=\frac{2196}{1458}\)

 \(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\)\(\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

\(=\frac{729}{729}+\frac{243}{729}+\)\(\frac{81}{729}+\frac{27}{729}+\frac{9}{729}+\)\(\frac{3}{729}\)\(+\frac{1}{729}\)

\(=\frac{1093}{729}\)

đặt biểu thức trên là A

ta có : 

A= ghi biểu thức ra

A.3=3.(1+1/3+1/9+1/27+1/81+1/243+1/729)

A.3=3+1+1/3+1/9+1/27+1/81+1/243

A.3-A=...

A.2=3-1/729

sau đó bn tự tính ra

1093/729

\(A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

\(3\times A=3+1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)

\(3\times A-A=3-\frac{1}{729}=\frac{2186}{729}\)

\(2\times A=\frac{2186}{729}=>A=\frac{1093}{729}\)

1 + 1/3 + 1/9+1/27+1/81+1/243+1/729

=1+1-1/3+1/3-1/9+1/9-1/27-1/27-1/81+1/81-1/243

= 2 - 1/243

=485/243

S = 1/3+1/9+1/27+1/81+1/243+1/729+1/2187 ( 1 ) 
Nhân S với 3. Ta có: 
S x 3 = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 ( 2 ) 
Trừ ( 2 ) với ( 1 ) ta có: 
S x 3 - S = 1 - 1/ 2187 
2S = 2186/ 2187 
S = 2186/ 2187 : 2 
S = 1093/ 2187 

là121/243

2 điểm!?

thi hay sao?

S= 1/1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729

S= 3 x ( 1/1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 )

S = 3 +1 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729

S= 3 +1 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 - 1 - 1/9 -1/27 - 1/81 - 1/243 - 1/729

S = 3 - 1/729 

S= 142/729

\(=1\frac{364}{729}\)\(=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}=1+\frac{243}{729}+\frac{81}{729}+\frac{27}{729}+\frac{9}{729}+\frac{3}{729}+\frac{1}{729}=1\frac{ }{ }\)

\(=1\frac{364}{729}\)