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a)A=2^0+2^1+2^2+....+2^2010
ta lay:2A=2^1+2^2+2^3+...+2^2011
ta lay:2A-A=(2^1+2^2+2^3+...+2^2011)-(2^0+2^1+2^3+...+2^2010)
=2^1+2^2+2^3+...+2^2011-2^0-2^1-2^2-2^3-...-2^2010
=2^2011-2^0=2^2011-1=A
Vay A=2^2011-1
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 20 + 21 +22 + 23 + ... + 22010
2A = 2 . ( 20 + 21 + 22 + 23 + ... + 22010 )
2A = 2 + 22 + 23 + 24 + ... + 22011
2A - A= ( 2 + 22 + 23 + 24 + ... + 22011 ) - ( 20 + 21 + 22 + 23 + ... + 22010 )
A = 22011 - 20
A = 22011 - 1
Vậy A = 22011 - 1
A=20 +21+22+23+...+22010
=>2A= 2+22+23+24+...+22011
=>2A-A=(2+22+23+24+...+22011)-(20+21+22+23+...+22010)
=>A=22011-1
Vậy A=22011-1
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt tổng đó = A. Ta có:
\(A=2^0+2^1+2^2+...+2^{2010}\)
\(2A=2^1+2^2+2^3+...+2^{2011}\)
\(A=2A-A\)
\(A=\left(2^1+2^2+2^3+...+2^{2011}\right)-\left(2^0+2^1+2^2+...+2^{2010}\right)\)
\(A=2^{2011}-1\)
Gọi tổng này là A
Ta có: 2A = \(2+2^2+2^3+...+2^{2011}\)
A = \(1+2+2^2+...+2^{2010}\)
\(\Rightarrow\) A = \(2^{2011}-1\)
Chúc bạn học tốt !!!!
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 20 + 21 + 22 + ... + 22010
2A = 21 + 22 + ... + 22010 + 22011
2A - A = 22011 - 20
A = 22011 - 1
\(A=2^0+2^1+2^2+..+2^{2010}\)
\(\Rightarrow2A=2^1+2^2+2^3+...+2^{2011}\)
\(\Rightarrow2A-A=2^{2011}-2^0\)
\(A=2^{2011}-1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Cho \(A=2^0+2^1+...+2^{2009}+2^{2010}\)
-> \(2A=2^1+2^2+...+2^{2010}+2^{2011}\)
\(2A-A=2^1+2^2+...+2^{2011}-\left(2^0+2^1+...+2^{2010}\right)\)
\(A=2^{2011}-2^0\)
\(A=2^{2011}-1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 2o + 21 + 22 + ... + 22010
=> 2A = 21 + 22 + 23 + ... + 22010 + 22011
Mà A = 20 + 21 + 22 + ... + 22010
=> 2A - A = A = 1 + 22011
B = 1 + 3 + 32 + ... + 3100
=> 3B = 3 + 32 + 33 + ... + 3100 + 3101
Mà B = 1 + 3 + 32 + ... + 3100
=> 3B - B = 2B = 2 + 3101
=> B = ( 2 + 3101 ) : 2
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Help Me
Tui cần gấp
Đúng tui k nhưng làm hẳn ra nha :)
Nếu lâu thì làm mẫu 1 vài phần OK :)
a) \(2A=2^1+2^2+2^3+...+2^{2010}\)
=> \(2A-A=2^{2011}-2^0\Leftrightarrow A=2^{2011}-1\)
b) \(3B=3+3^2+3^3+3^4+...+3^{101}\)
=> \(3B-B=3^{101}-1\Leftrightarrow2B=3^{101}-1\Leftrightarrow B=\frac{1}{2}\left(3^{101}-1\right)\)
Tương tự Cx4, Dx5
A= 2^0 + 2^1 + 2^2 + ... + 2^2010
=> 2A = 2^1 + 2^2 + 2^3 + ... + 2^2011
=> 2A - A = 2^2011 - 2^0
=> A = 2^2011 - 1
A = 2^0 + 2^1 + 2^2 + 2^3 +...+ 2^2010
2A = 2^1 + 2^2 + 2^3 + 2^4 +...+ 2^2011
2A - A = ( 2^1 + 2^2 + 2^3 + 2^4 +...+ 2^2011 ) - ( 1 + 2^2 + 2^3 +...+ 2^2010 )
A = 2^2011 - 1