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

=\(1+\frac{1}{3^1}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+\frac{1}{3^5}+\frac{1}{3^6}\)

=\(\frac{3^6}{3^6}+\frac{3^5}{3^6}+\frac{3^4}{3^6}+\frac{3^3}{3^6}+\frac{3^2}{3^6}+\frac{3^1}{3^6}+\frac{3^0}{3^6}\)

=\(\frac{3^6+3^5+3^4+3^3+3^2+3+1}{3^6}\)

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

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

nha.

tong cua day so tren la 1093/729

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

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

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

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

gọi biểu thức trên là A

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

          \(\frac{1}{3}\)x  A =\(\frac{1}{3}\)+\(\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}+\frac{1}{2187}\)   (2)           

lấy (1) - (2)

           \(\frac{2}{3}xA\)=  1 - \(\frac{1}{2187}\)

            \(\frac{2}{3}xA\)= \(\frac{2186}{2187}\)

                  A       =  \(\frac{2186}{2187}:\frac{2}{3}\)

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

Đặt B = 1/3 + 1/9 + 1/27 + 1/81 +1/243 + 1/729 + 1/2187

B x 3 = 3 x ( 1/3 + 1/9 +.......+ 1/729 + 1/2187)

        =  1 + 1/3 + 1/9 +.........+1/243 +1/729 

Lấy B x 3 - B ta có :

B x 3 - B = 1 + 1/3 +1/9+ .........+1/243 + 1/729 - 1/3 + 1/9 +.........+1/729 +1/2187

B x (3 - 1)= 1 - 1/2187

B x  2     =   2186/2187

B       = 2186/2187 : 2 = 1093/2187

b) 1/3+1/3^2+1/3^3+1/3^4+1/3^5 (goi tong bang M)

3M=1+1/3+1/3^2+1/3^3+1/3^4

3M-M=1-1/3^5

2M=242/243

M=242/243*1/2=121/243

^ là gì vậy 

2186/729 nha bn k mk đi

A=1+1/3+1/9+...+1/729

3A=3+1+1/3+....+1/243

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

2A=3-1/729

A=(3-1/729)/2

k cho mình nha

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

Ta thấy tất cả phân số này đều có mẫu chung là 81

=> A = \(\frac{81}{81}\)+ \(\frac{27}{81}\)+ \(\frac{9}{81}\)+\(\frac{3}{81}\)+ \(\frac{1}{81}\)( lấy 81 chia cho mẫu rồi nhân cho tử, đặt mẫu số là 81 )

=> A = \(\frac{81+27+9+3+1}{81}\)= \(\frac{121}{81}\)

nhớ ủng hộ mik với nha mn

=121/81 nhé bạn

\(\frac{34642}{34911}\)

nhanh mình k 

\(A=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+...+\frac{1}{6561}\)

\(\Rightarrow A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+...+\frac{1}{3^8}\)

\(\Rightarrow3A=3.\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^8}\right)\) \(=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\)

\(\Rightarrow3A-A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}-\frac{1}{3}-\frac{1}{3^2}-\frac{1}{3^3}-...-\frac{1}{3^8}\)

\(\Rightarrow2A=1-\frac{1}{3^8}\) \(\Rightarrow A=\frac{1-\frac{1}{3^8}}{2}\)

k cho mik đi mn!Nguyễn Như Quỳnh!

Sao mà mình hỏi bài này từ lâu lắm rồi mà vẫn chưa có bạn nào trả lời nhỉ?

     A)   \(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}\)

2A= \(1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}\)

2A-A = \(1-\dfrac{1}{32}\)

A=  \(\dfrac{31}{32}\)