\(A=3^2+3^3+3^4+...........+3^{2006}\)
\(\Leftrightarrow3A=3^3+3^4+3^5+................+3^{2006}+3^{2007}\)
\(\Leftrightarrow3A-A=\left(3^3+3^4+3^5+.........+3^{2007}\right)-\left(3^2+3^3+..........+3^{2006}\right)\)
\(\Leftrightarrow2A=3^{2007}-3^2\)
Đến đây thì tịt ngẩm!
\(A=3^2+3^3+...+3^{2006}\)
\(\Rightarrow3A=3^3+3^4+...+3^{2007}\)
\(\Rightarrow3A-A=\left(3^3+3^4+...+3^{2007}\right)-\left(3^2+3^3+...+3^{2006}\right)\)
\(\Rightarrow2A=3^{2007}-3^2\)
Do \(2A+3=3x\)
\(\Rightarrow3^{2007}-3^2+3=3x\)
\(\Rightarrow3^{2007}-6=3x\)
\(\Rightarrow x=3^{2006}-2\)
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