Đặt \(A=2^{2009}+2^{2008}+...+2+1\)
\(\Rightarrow2A=2^{2010}+2^{2009}+...+2^2+1\)
\(\Rightarrow2A-A=\left(2^{2010}+2^{2009}+...+2^2+1\right)-\left(2^{2009}+2^{2008}+...+2+1\right)\)
\(\Rightarrow A=2^{2010}-1\)
Ta có: \(M=2^{2010}-2^{2009}-2^{2008}-...-2-1\)
\(=2^{2010}-\left(2^{2009}+2^{2008}+...+2+1\right)\)
\(=2^{2010}-\left(2^{2010}-1\right)\)
\(=2^{2010}-2^{2010}+1=1\)
Vậy M = 1
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