1 + 2/   =

1+ 2/

1 + 2/3

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

\(\Rightarrow3A=3+1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)

\(\Rightarrow3A-A=3-\frac{1}{729}\)

\(\Rightarrow2A=\frac{2186}{729}\)

\(\Rightarrow A=\frac{2186}{729}:2=\frac{1093}{729}\)

\(A=\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}\\ =\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+\dfrac{1}{3^5}\\ =>3A=1+\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}\\ =>3A-A=2A=1-\dfrac{1}{3^5}\\ =>A=\dfrac{1-\dfrac{1}{3^5}}{2}=\dfrac{3^5-1}{2.3^5}\)

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

=>3A=1+1/3+...+1/81

=>2A=1-1/243=242/243

=>A=121/243

Đặt A= 1/3+1/9+1/27+1/81+1/243

A= 1/3+1/3^2+1/3^3+1/3^4+1/3^5

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

3A-A=1+1/3+1/3^2+1/3^3+1/3^4-1/3-1/3^2-1/3^3-1/3^4-1/3^5

2A=1-1/3^5

2A=242/243

A=121/243

ta bằng 121/243

duyệt nha

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

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

=\(\dfrac{243+81+27+3+1}{243}\)

=355/243

Lời giải:

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

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

$3A-A=3-\frac{1}{243}$

$2A=\frac{728}{243}$

$A=\frac{364}{243}$

1) ( 2016 . 2016 - 2013 . 2009 ) . X = 18

               ( 4064256 - 4044117 ) . X = 18

                                                0 . X = 18

                                                    X = 18 : 0

                                                    X = \(\varnothing\)

   Vậy X = \(\varnothing\)

2) ( \(\frac{1}{3}\) + \(\frac{1}{9}\) + \(\frac{1}{27}\) + \(\frac{1}{81}\) + \(\frac{1}{243}\) ) . X = \(\frac{2}{3}\)

        \(\frac{121}{243}\) . X = \(\frac{2}{3}\)

                 X = \(\frac{2}{3}\) : \(\frac{121}{243}\)

                 X = \(\frac{162}{121}\)

CHÚC BẠN HỌC TỐT

tổng các ps trên là ; \(\frac{364}{729}\)

đặt biểu thức đó là X

ta có :

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

\(\Rightarrow3X-X=1-\frac{1}{729}\)

\(\Rightarrow X=\frac{728}{729}.\frac{1}{2}=\frac{364}{729}\)