Ta có :
\(A=2^1+2^2+2^3+...+2^{2010}\)
\(=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{2009}+2^{2010}\right)\)
\(=\left(2.1+2.2\right)+\left(2^3.1+2^3.2\right)+...+\left(2^{2009}.1=2^{2009}.2\right)\)
\(=2.3+2^3.3+...+2^{2009}.3\)
\(\Leftrightarrow A⋮3\)
Ta có :
\(A=2^1+2^2+...+2^{2010}\)
\(=\left(2^1+2^2+2^3\right)+...+\left(2^{2008}+2^{2009}+2^{2010}\right)\)
\(=\left(2.1+2.2+2.2^2\right)+\left(2^4.1+2^4.2+2^4.2^2\right)+...+\left(2^{2008}.1+2^{2008}.2+2^{2008}.2^2\right)\)
\(=2.7+2^4.7+...+2^{2008}.7\)
\(\Leftrightarrow A⋮7\)
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