1+1/3+1/9+1/27+1/81+1/243 = ? . tính bằng cách thuận tiện
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NN
1
DD
Đoàn Đức Hà
Giáo viên
16 tháng 10 2021
\(A=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)
\(3\times A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(3\times A-A=\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\right)-\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\right)\)
\(2\times A=1-\frac{1}{729}=\frac{728}{729}\)
\(A=\frac{364}{729}\)
H
2
U
21 tháng 7 2018
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}+\frac{1}{32}-\frac{1}{64}\)
\(A=1-\frac{1}{64}\)
\(A=\frac{63}{64}\)
\(B=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(3B=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)
\(3B-B=1-\frac{1}{243}\)
\(2B=\frac{242}{243}\)
\(B=\frac{242}{243}\div2\)
\(B=\frac{121}{243}\)
21 tháng 7 2018
a.A=1/2+1/4+1/8+1/16+1/32+1/64
A= \(\frac{1}{1\cdot2}+\frac{1}{2\cdot2}+\frac{1}{2\cdot4}+\frac{1}{4\cdot4}+\frac{1}{4\cdot8}+\frac{1}{8\cdot8}\)
= \(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{8}\)
= 1 - 1/8 = 7/8
b.B=1/3+1/9+1/27+1/81+1/243
B= \(\frac{1}{1\cdot3}+\frac{1}{3\cdot3}+\frac{1}{3\cdot9}+\frac{1}{9\cdot9}+\frac{1}{9\cdot27}\)
= 1 - 1/27 = 26/27
HH
1
C
17 tháng 4 2022
= 1 x 27/3x27 + 1x9/9x9 + 1x3 / 27 x 3 + 1/81
=27/81 + 9/81 + 3/81 + 1/81
= 40/81
5 tháng 10 2016
Đặt \(A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^5}\)
\(3A=3\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^5}\right)\)
\(3A=3+1+...+\frac{1}{3^4}\)
\(3A-A=\left(3+1+...+\frac{1}{3^4}\right)-\left(1+\frac{1}{3}+...+\frac{1}{3^5}\right)\)
\(2A=3-\frac{1}{3^5}\)
\(A=\frac{3-\frac{1}{3^5}}{2}\)
5 tháng 10 2016
Đặt \(S=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(S=1+\frac{1}{1\times3}+\frac{1}{3\times3}+\frac{1}{9\times3}+\frac{1}{27\times3}+\frac{1}{81\times3}\)
\(S\times3=\left(1+\frac{1}{1\times3}+\frac{1}{3\times3}+\frac{1}{9\times3}+\frac{1}{27\times3}+\frac{1}{81\times3}\right)\times3\)
\(S\times3=3+1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)
Xét: \(S\times3-S=\left(3+1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\right)-\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\right)\)
\(S\times2=3-\frac{1}{243}\)
\(S\times2=\frac{728}{243}\)
\(S=\frac{728}{243}\div2\)
\(S=\frac{364}{243}\)
Vậy \(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}=\frac{364}{243}\)
DM
2
13 tháng 5 2021
= 27/81 + 9/81 + 3/81 + 1/81
= ( 27/81 + 3/81 ) + ( 9/81 + 1/81 )
= 30/81 + 10/81
= 40/81
# Math is easy
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
20 tháng 9
(\(\dfrac{2}{3}\) + \(\dfrac{8}{9}\) + \(\dfrac{26}{27}\) + \(\dfrac{80}{81}\) + \(\dfrac{242}{243}\)) : y = 5
Đăt A = \(\dfrac{2}{3}\) + \(\dfrac{8}{9}\) + \(\dfrac{26}{27}\) + \(\dfrac{80}{81}\) + \(\dfrac{242}{243}\)
3A = 2 + \(\dfrac{8}{3}\) + \(\dfrac{26}{9}\) + \(\dfrac{80}{27}\) + \(\dfrac{242}{81}\)
3A - A = 2 + \(\dfrac{8}{3}\) + \(\dfrac{26}{9}\) + \(\dfrac{80}{27}\) + \(\dfrac{242}{81}\) - \(\dfrac{2}{3}\)-\(\dfrac{8}{9}\)-\(\dfrac{26}{27}\)-\(\dfrac{80}{81}\)-\(\dfrac{242}{243}\)
A x (3 - 1) = 2 - \(\dfrac{242}{243}\)+ (\(\dfrac{8}{3}\) - \(\dfrac{2}{3}\))+(\(\dfrac{26}{9}\) - \(\dfrac{8}{9}\))+(\(\dfrac{80}{27}\)-\(\dfrac{26}{27}\))+(\(\dfrac{242}{81}\)-\(\dfrac{80}{81}\))-\(\dfrac{242}{243}\)
A x 2 = 2 - \(\dfrac{242}{243}\) + 2 + 2 + 2 + 2
A x 2 = (2 + 2 + 2 +2 + 2) - \(\dfrac{242}{243}\)
A x 2 = 2x5 - \(\dfrac{242}{243}\)
A x 2 = 10 - \(\dfrac{242}{243}\)
A x 2 = \(\dfrac{2188}{243}\)
A = \(\dfrac{2188}{243}\) : 2
A = \(\dfrac{1094}{243}\)
\(\dfrac{1094}{243}\) : y = 5
y = \(\dfrac{1094}{243}\) : 5
y = \(\dfrac{1094}{1215}\)
LB
1
10 tháng 7 2015
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
TH
3
16 tháng 3 2016
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
1+ 1 /3+1/9+1/27+1/81+1/243+1/729.
Đặt:
S = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243
Nhân S với 3 ta có:
S x 3 = 3 +1+ 1/3 + 1/9 + 1/27 + 1/81
Vậy:
S x 3 - S = 3 - 1/243
2S = 728/243
S = 364/243
tick đúng nha
=364/243