S=1/3+1/9+1/27+1/81
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\(3S=241+81+27+9+...+\dfrac{1}{9}+\dfrac{1}{27}\)
\(2S=3S-S=241-\dfrac{1}{81}=\dfrac{241x81-1}{81}\)
\(\Rightarrow S=\dfrac{241x81-1}{2x81}\)
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
\(S=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)
\(3\times S=3+1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(3\times S-S=\left(3+1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\right)-\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\right)\)
\(2\times S=3-\frac{1}{729}\)
\(S=\frac{1093}{729}\)
(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 = \(\dfrac{4}{81}\)
\(\left(y+\dfrac{1}{3}\right)+\left(y+\dfrac{1}{9}\right)+\left(y+\dfrac{1}{27}\right)+\left(y+\dfrac{1}{81}\right)=\dfrac{56}{81}\)
\(\Rightarrow y+\dfrac{1}{3}+y+\dfrac{1}{9}+y+\dfrac{1}{27}+y+\dfrac{1}{81}=\dfrac{56}{81}\)
\(\Rightarrow4\times y+\dfrac{40}{81}=\dfrac{56}{81}\)
\(\Rightarrow4\times y=\dfrac{56}{81}-\dfrac{40}{81}\)
\(\Rightarrow4\times y=\dfrac{16}{81}\)
\(\Rightarrow y=\dfrac{16}{81}:4\)
\(\Rightarrow y=\dfrac{4}{81}\)
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 ~