LA
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K
Khách
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PA
2
16 tháng 10 2023
\(3A=3\cdot\left(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}+\dfrac{1}{729}\right)\)
\(\Rightarrow3A=1+\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}\)
Lấy \(3A-A=1-\dfrac{1}{729}\)
\(\Rightarrow2A=\dfrac{728}{729}\Rightarrow A=\dfrac{364}{729}\)
16 tháng 10 2023
A=1/3+1/9+1/27+1/81+1/243+1/729
3A=1+1/3+1/9+1/27+1/81+1/243
3A-A=(1+1/3+1/9+1/27+1/81+1/243)-(1/3+1/9+1/27+1/81+1/243+1/729)
3A-A=1-1/3+1/3-1/9+1/9-1/27+1/27-1/81+1/81-1/243+1/243-1/729)
2A=1-1/729
2A=728/729
A=728/729/2
A=364/729
A
3
27 tháng 7 2016
Đặt \(A=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)
\(3A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(3A-A=\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\right)-\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\right)\)
\(2A=1-\frac{1}{729}=\frac{728}{729}\)
\(A=\frac{728}{729}:2=\frac{728}{729}.\frac{1}{2}=\frac{364}{729}\)
DT
1
3 tháng 5 2015
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
LN
2
12 tháng 5 2017
\(A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)
\(3\times A=3+1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(3\times A-A=3-\frac{1}{729}=\frac{2186}{729}\)
\(2\times A=\frac{2186}{729}=>A=\frac{1093}{729}\)
11 tháng 4 2017
\(=1\frac{364}{729}\)\(=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}=1+\frac{243}{729}+\frac{81}{729}+\frac{27}{729}+\frac{9}{729}+\frac{3}{729}+\frac{1}{729}=1\frac{ }{ }\)
TT
4
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
5 tháng 5 2023
\(x\) \(\times\) \(\dfrac{1}{4}\) = 6 : 1 : 2
\(x\) \(\times\) \(\dfrac{1}{4}\) = 6:2
\(x\) \(\times\) \(\dfrac{1}{4}\) = 3
\(x\) = 3 : \(\dfrac{1}{4}\)
\(x\) = 12
N
5
12 tháng 5 2017
\(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)
\(=\frac{729}{729}+\frac{243}{729}+\frac{81}{729}+\frac{27}{729}+\frac{9}{729}+\frac{3}{729}+\frac{1}{729}\)
\(=\frac{729+243+81+27+9+3+1}{729}\)
\(=\frac{1087}{729}\)
12 tháng 5 2017
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 \(A=\left(3-\frac{1}{729}\right):2=\frac{3}{2}-\frac{1}{1458}=\frac{2197}{1458}-\frac{1}{1458}=\frac{2196}{1458}\)
20 tháng 3 2016
\(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)
=\(1+\frac{1}{3^1}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+\frac{1}{3^5}+\frac{1}{3^6}\)
=\(\frac{3^6}{3^6}+\frac{3^5}{3^6}+\frac{3^4}{3^6}+\frac{3^3}{3^6}+\frac{3^2}{3^6}+\frac{3^1}{3^6}+\frac{3^0}{3^6}\)
=\(\frac{3^6+3^5+3^4+3^3+3^2+3+1}{3^6}\)
=\(\frac{729+243+81+27+9+3}{729}\)
=\(\frac{1093}{729}\)
nha.
Đặt A = 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729
A x 3 = 3 x (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729)
= 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243
A x 3 - A = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729)
= 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - 1/3 - 1/9 - 1/27 - 1/81 - 1/243 - 1/729
= 1 - 1/729
A x 2 = 728/729
A = 364/729