JK
1
K
Khách
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TT
1
DA
17 tháng 5 2020
A=\(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\)\(\frac{1}{2^{2019}}\)
2A= \(2\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2019}}\right)\)
2A= \(2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2018}}\)
2A-A=\(\left(1+2+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2018}}\right)\)\(-\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2019}}\right)\)
A= \(2-\frac{1}{2^{2019}}\)
A=\(\frac{2^{2020}}{2^{2019}}-\frac{1}{2^{2019}}\)
A=\(\frac{2^{2020}-1}{2^{2019}}\)
30 tháng 1 2019
\(A=1+2^1+2^2+...+2^{2017}\)
\(2A=2+2^2+2^3+...+2^{2018}\)
\(2A-A=2^{2018}-1hayA=2^{2018}-1\)
2; 3 tuong tu
30 tháng 1 2019
1) A = 1 + 2 + 22 + 23 + .... + 22018
2A = 2 + 22 + 23 + 24 + ..... + 22019
2A - A = ( 2 + 22 + 23 + 24 + ..... + 22019 ) - ( 1 + 2 + 22 + 23 + .... + 22018 )
Vậy A = 22019 - 1
2) B = 1 + 3 + 32 + 33 + ..... + 32018
3A = 3 + 32 + 33 + ...... + 32019
3A - A = ( 3 + 32 + 33 + ...... + 32019 ) - ( 1 + 3 + 32 + 33 + ..... + 32018 )
2A = 32019 - 1
Vậy A = ( 32019 - 1 ) : 2
3) C = 1 + 4 + 42 + 43 + ...... + 42018
4A = 4 + 42 + 43 + ...... + 42019
4A - A = ( 4 + 42 + 43 + ...... + 42019 ) - ( 1 + 4 + 42 + 43 + ...... + 42018 )
3A = 42019 - 1
Vậy A = ( 42019 - 1 ) : 3
HN
8
6 tháng 5 2015
\(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\)
\(2A=2+1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2011}}\)
\(2A-A=\left(2+1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\right)\)
\(2A-A=2-\frac{1}{2^{2012}}\Rightarrow A=2-\frac{1}{2^{2012}}\)
\(A=\frac{2^{2013}}{2^{2012}}-\frac{1}{2^{2012}}=\frac{2^{2012}+1}{2^{2012}}\)
P
0
HK
1
8 tháng 5 2015
A= 1+ 1/2 + 1/22 + ... + 1/22012
(1/2)A= 1/2+1/22+...+1/22013
A-(1/2)A= (1+ 1/2 + 1/22 + ... + 1/22012) - ( 1/2+1/22+...+1/22013)
(1/2)A = 1 - 1/22013
A= (1- 1/22013) : 1/2
A= 2 - 1/22012
TV
2
16 tháng 3 2018
A = 1 + 1/22+1/23+...+1/22015
(1-1/2) A = (1-1/2) (1+1/22+1/23+...+1/22015) = 1 - 1/22016
A = 2 *( 1 -1/22016) = 2 -1/22015
19 tháng 4 2018
A = 1 + 1/22+1/23+...+1/22015
(1-1/2) A = (1-1/2) (1+1/22+1/23+...+1/22015) = 1 - 1/22016
A = 2 *( 1 -1/22016) = 2 -1/22015
DT
1
BQ
3
KT
11 tháng 5 2018
\(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{2012}}\)
\(\Leftrightarrow\)\(2A=2+1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{2011}}\)
\(\Rightarrow\)\(2A-A=\left(2+1+\frac{1}{2}+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{2012}}\right)\)
\(\Rightarrow\)\(A=2-\frac{1}{2^{2012}}\)
11 tháng 5 2018
\(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\)
\(\Rightarrow2A=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\)
\(\Rightarrow2A-A=\left(2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\right)\)
\(\Rightarrow A=2-\frac{1}{2^{2012}}\)
TL
10
2 tháng 8 2016
=>2A=2+1+1/2+1/22+...+1/22011
=>2A-A=(2+1+1/2+1/22+...+1/22011)-(1+1/2+1/22+1/23+...+1/22012)
=>A=2-1/22012
2 tháng 8 2016
Bài 2 : Rút gọn biểu thức
A = 1 + 1/2 + 1/22 + 1/23 + ... + 1/22012
=>2A=2+1+1/2+1/22+...+1/22011
=>2A-A=(2+1+1/2+1/22+...+1/22011)-(1+1/2+1/22+1/23+...+1/22012)
=>A=2-1/22012
A= 1/2+1/22+1/23+1/24+.....+1/22019
2A= 1+1/2+1/22+1/23+1/24+.....+1/22018
2A-A=(1+1/2+1/22+1/23+1/24+.....+1/22018)-(1/2+1/22+1/23+1/24+.....+1/22019)
A=1-1/22019