Tính: M=2^2010-(2^2009+2^2008+...+2^1+2^0)
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Tính: M= 2^2010-( 2^2009 + 2^2008+....+2^1 +2^0)
Đặt N = 22009 + 22008 + 22007 +......+ 21 + 20
2N = 22010 + 22009 + 22008 +.....+ 22 + 21
2N - N = 22010 - 20
=> N = 22010 - 1
=> M = 22010 - (22010 - 1)
=> M = 22010 - 22010 + 1
=> M = 1
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tính:
\(M=2^{2010}-\left(2^{2009}+2^{2008}+...+2^1+2^0\right)\)
Đặt \(A=2^{2009}+2^{2008}+...+2^1+2^0\)
Ta có : \(2A=2^{2010}+2^{2009}+...+2^2+2^1\)
\(\Rightarrow2A-A=2^{2010}-2^0\Rightarrow A=2^{2010}-1\)
Do đó : \(M=2^{2010}-A=2^{2010}-\left[2^{2010}-1\right]=1\)
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\(M=2^{2010}-\left(2^{2009}+2^{2008}+...+2^1+2^0\right)\)
\(2^{2010}-M=2^{2009}+2^{2008}+...+2+1\)
\(2\left(2^{2010}-M\right)=2\left(2^{2009}+2^{2008}+...+2+1\right)\)
\(2\left(2^{2010}-M\right)=2^{2010}+2^{2009}+...+2^2+2\)
\(2\left(2^{2010}-M\right)-M=\left(2^{2010}+2^{2009}+...+4+2\right)-\left(2^{2009}+2^{2008}+...+2+1\right)\)
\(2^{2010}-M=2^{2010}+2^{2009}+...+4+2-2^{2009}-2^{2008}-...-2-1\)
\(2^{2010}-M=2^{2010}-1\)
=> M = 1
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Tính: 2^2010 - (2^2009 + 2^2008+ .....+ 2^1 + 2^0)
Đặt A = 22009 + 22008 + ... + 21 + 20
2A = 22010 + 22009 + ... + 22 + 21
2A - A = (22010 + 22009 + ... + 22 + 21) - (22009 + 22008 + ... + 21 + 20)
A = 22010 - 20
A = 22010 - 1
=> 22010 - (22009 + 22008 + ... + 21 + 20)
= 22010 - (22010 - 1)
= 22010 - 22010 + 1
= 1
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Đặt A = 22009 + 22008 + ... + 21 + 20
2A = 22010 + 22009 + ... + 22 + 21
2A - A = (22010 + 22009 + ... + 22 + 21) - (22009 + 22008 + ... + 21 + 20)
A = 22010 - 20
A = 22010 - 1
=> 22010 - (22009 + 22008 + ... + 21 + 20)
= 22010 - (22010 - 1)
= 22010 - 22010 + 1
= 1
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tính 2010*2010-2009*2009+2008*2008-........+2*2-1*1
M=2^2010-(2^2009+2^2008+...+2^1+2^0)
Tính M=22010- (22009+22008+.......+21+20)
Tìm m = 2^2010 - ( 2^2009 + 2^2008 + .... + 2^1 + 2^0 )
\(M=2^{2010}-\left(2^{2009}+2^{2008}+...+2^1+2^0\right)\)
\(2^{2010}-M=1+2+2^2+...+2^{2008}+2^{2009}\)
\(2\left(2^{2010}-M\right)=2+2^2+2^3+...+2^{2009}+2^{2010}\)
\(2\left(2^{2010}-M\right)-\left(2^{2010}-M\right)=\left(2+2^2+2^3+...+2^{2009}+2^{2010}\right)-\left(1+2+2^2+...+2^{2008}+2^{2009}\right)\)
\(2^{2010}-M=2^{2010}-1\)
\(M=2^{2010}-2^{2010}+1\)
\(M=1\)
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Đặt \(M=2^{2010}-A\)
Ta có:
\(A=2^{2009}+2^{2008}+...+2^1+2^0\)
\(\Rightarrow2A=2^{2010}+2^{2009}+...+2^2+2^1\)
\(\Rightarrow2A-A=\left(2^{2010}+2^{2009}+...+2^2+2^1\right)-\left(2^{2009}+2^{2008}+...+2^1+2^0\right)\)
\(\Rightarrow A=2^{2010}-1\)
\(\Rightarrow M=2^{2010}-\left(2^{2010}-1\right)\)
\(\Rightarrow M=\left(2^{2010}-2^{2010}\right)+1\)
\(\Rightarrow M=1\)
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1.Tính:
\(M=2^{2010}-\left(2^{2009}+2^{2008}+...+2^{10}+2^0\right)\)
\(M=2^{2010}-2^{2009}-2^{2008}-...-2^1-2^0\)
\(-M=-\left(2^{2010}-2^{2009}-2^{2008}-...-2^1-2^0\right)\)
\(-M=2^{2010}+2^{2009}+2^{2008}+...+2^1+2^0\)
\(-2M=2.\left(2^{2010}+2^{2009}+2^{2008}+...+2^1+2^0\right)\)
\(-2M=2^{2011}+2^{2010}+2^{2009}+...+2^2+2^1\)
\(-M=2^{2011}+2^{2010}+...+2^2+2^1-\left(2^{2010}+2^{2009}+2^{2008}+...+2^1+2^0\right)\)
\(-M=2^{2011}-1=>M=-2^{2011}+1\)
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tại sao lại có dấu ''-'' vậy bạn mình không hiểu lắm.
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Tính:
M= 22010-( 22009+22008+...+21+20)
\(M=2^{2010}-\left(2^{2009}+2^{2008}+...+2^1+2^0\right)\)
\(2^{2010}-M=2^{2009}+2^{2008}+...+2^1+2^0\)
\(2\left(2^{2010}-M\right)=2^1+2^2+....+2^{2009}+2^{2010}\)
\(2\left(2^{2010}-M\right)-\left(2^{2010}-M\right)=\left(2^1+2^2+....+2^{2009}+2^{2010}\right)-\left(2^0+2^1+...+2^{2008}+2^{2009}\right)\)
\(2^{2010}-M=2^{2010}-1\)
\(M=2^{2010}-2^{2010}+1\)
\(M=1\)
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M=22010-(22009+22008+22007+...+21+20)
M=22010-22009-22008-22007-...-21-20
=>2M=22011-22010-22009-22008-...-22-21
=>2M-M=22011-22010-22009-22008-...-22-21-(22010-22009-22008-22007-...-21-20)
=>M=22011-22010-22009-22008-...-22-21-22010+22009+22008+22007+...+21+20
=22011-22010-22010+20
=22011-2.22010+1
=22011-22011+1
=1
Vậy M=1
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