\(3S=241+81+27+9+...+\dfrac{1}{9}+\dfrac{1}{27}\)

\(2S=3S-S=241-\dfrac{1}{81}=\dfrac{241x81-1}{81}\)

\(\Rightarrow S=\dfrac{241x81-1}{2x81}\)

Sửa đề: 1/729

S=1+1/3+...+1/729

=1+1/3+...+(1/3)^6

=>3S=3+1+...+(1/3)^5

=>2S=3-(1/3)^6=(3^7-1)/3^6

=>S=(3^7-1)/(3^6*2)

= 1 x 27/3x27 + 1x9/9x9 + 1x3 / 27 x 3 + 1/81

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

= 40/81

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 

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

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

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

\(3\times S-S=\left(3+1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\right)-\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\right)\)

\(2\times S=3-\frac{1}{729}\)

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

(y + \(\dfrac{1}{3}\)) + ( y + \(\dfrac{1}{9}\)) + ( y + \(\dfrac{1}{27}\)) + ( y + \(\dfrac{1}{81}\)) = \(\dfrac{56}{81}\)

( y + y + y + y ) + (\(\dfrac{1}{3}\)+ \(\dfrac{1}{9}\) + \(\dfrac{1}{27}\) + \(\dfrac{1}{81}\)) = \(\dfrac{56}{81}\)

4\(y\) + ( \(\dfrac{27}{81}\) + \(\dfrac{9}{81}\) + \(\dfrac{3}{27}\) + \(\dfrac{1}{81}\) ) = \(\dfrac{56}{81}\)

4y + \(\dfrac{40}{81}\) = \(\dfrac{56}{81}\)

4y = \(\dfrac{56}{81}\) - \(\dfrac{40}{81}\)

4y = \(\dfrac{16}{81}\)

y  = \(\dfrac{16}{81}\) : 4

y = \(\dfrac{4}{81}\)

\(\left(y+\dfrac{1}{3}\right)+\left(y+\dfrac{1}{9}\right)+\left(y+\dfrac{1}{27}\right)+\left(y+\dfrac{1}{81}\right)=\dfrac{56}{81}\)

\(\Rightarrow y+\dfrac{1}{3}+y+\dfrac{1}{9}+y+\dfrac{1}{27}+y+\dfrac{1}{81}=\dfrac{56}{81}\)

\(\Rightarrow4\times y+\dfrac{40}{81}=\dfrac{56}{81}\)

\(\Rightarrow4\times y=\dfrac{56}{81}-\dfrac{40}{81}\)

\(\Rightarrow4\times y=\dfrac{16}{81}\)

\(\Rightarrow y=\dfrac{16}{81}:4\)

\(\Rightarrow y=\dfrac{4}{81}\)

\((y+\dfrac{1}{3})+(y+\dfrac{1}{9})+(y+\dfrac{1}{27})+(y+\dfrac{1}{81})=\dfrac{56}{81}\)

\(=>4y+(\dfrac{1}{3}+\dfrac{1}{9]+\dfrac{1}{27}+\dfrac{1}{81})=\dfrac{56}{81}\)

\(=>4y+\dfrac{1}{3}(1+\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27})=\dfrac{56}{81}\)

\(=>4y+\dfrac{1}{2}(1+\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}-\dfrac{1}{3}-\dfrac{1}{9}-\dfrac{1}{27}-\dfrac{1}{81})=\dfrac{56}{81}\)

\(=>4y+\dfrac{1}{2}(1-\dfrac{1}{81})=\dfrac{56}{81}\)

\(=>4y+\dfrac{1}{2}\times\dfrac{80}{81}=\dfrac{56}{81}\)

\(=>4y+\dfrac{40}{81}=\dfrac{56}{81}\)

\(=>4y=\dfrac{56}{81}-\dfrac{40}{81}\)

\(=>4y=\dfrac{16}{81}\)

\(=>y=\dfrac{4}{81}\)

121/81

\(=\frac{121}{81}\)

\(A=1+\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}\) \(\Rightarrow3A=3+1+\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}\)

\(\Rightarrow3A-A=3-\dfrac{1}{81}\Rightarrow2A=\dfrac{242}{81}\Rightarrow A=\dfrac{121}{81}\)

a) (x+1)/3 + (x+1)/9 + (x+1)/27 + (x+1)/81 = 56/81 
<=> (27x+27)/81 + (9x+9)/81 + (3x+3)/81 + (x+1)/81 = 56/81 (quy đồng) 
<=> 27x + 9x + 3x + x + 27 + 9 + 3 + 1 = 56 (khử mẫu) 
<=> 40x = 56- 40 = 16 
<=> x = 16/40 = 2/5 

~ hok tốt ~

Đ/s:\(\frac{2}{5}\)

~Hok tốt~

#)Giải :

 \(\left(y+\frac{1}{3}\right)+\left(y+\frac{1}{9}\right)+\left(y+\frac{1}{27}\right)+\left(y+\frac{1}{81}\right)=\frac{56}{81}\)

                                        \(4y+\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\right)=\frac{56}{81}\)

                                     \(4y+\left(\frac{27}{81}+\frac{9}{81}+\frac{3}{81}+\frac{1}{81}\right)=\frac{56}{81}\)

                                                                               \(4y+\frac{40}{81}=\frac{56}{81}\)

                                                                                      \(\Leftrightarrow4y=\frac{16}{81}\)

                                                                                         \(\Leftrightarrow y=\frac{4}{81}\)