\(A=3+3^2+3^3+...+3^{2008}\)
\(3A=3\left(3+3^2+3^3+...+3^{2008}\right)\)
\(3A=3^2+3^3+3^4+...+3^{2009}\)
\(3A-A=\left(3^2+3^3+3^4+...+3^{2009}\right)-\left(3+3^2+3^3+...+3^{2008}\right)\)
\(2A=3^{2009}-3\)
\(2A+3=3x\)
\(\Rightarrow3^{2009}-3+3=3x\)
\(\Rightarrow3^{2009}=3x\)
\(\Rightarrow x=3^{2008}\)
\(A=3+3^2+3^3+............+3^{2008}\)
\(\Leftrightarrow3A=3^2+3^3+............+3^{2008}+3^{2009}\)
\(\Leftrightarrow3A-A=\left(3^2+3^3+...........+3^{2009}\right)-\left(3+3^2+..........+3^{2008}\right)\)
\(\Leftrightarrow2A=3^{2009}-3\)
\(\Leftrightarrow2A+3=3^{2009}\)
\(\Leftrightarrow3^{2009}=3^x\)
\(\Leftrightarrow x=3^{2009}\left(tm\right)\)
Vậy ..................
