\(A=3+3^2+3^3+...+3^{2008}\)
\(\Rightarrow3A=3\cdot\left(3+3^2+3^3+...+3^{2008}\right)\)
\(\Rightarrow3A=3^2+3^3+3^4+...+3^{2009}\)
\(\Rightarrow3A-A=\left(3^2+3^3+3^4+...+3^{2009}\right)-\left(3+3^2+3^3+...+3^{2008}\right)\)
\(\Rightarrow2A=3^{2009}-3\)
Ta có: \(2A+3=3^x\)
\(\Rightarrow3^{2009}-3+3=3^x\)
\(\Rightarrow3^{2009}=3^x\)
\(\Rightarrow x=2009\)
Trả lời :
Nhân hai vế với 3 , ta được :
\(3A=3^2+3^3+3^4+...+3^{2009}\) ( 2 )
- \(A=3+3^2+3^3+...+3^{2008}\) ( 1 )
__________________________________________
\(2A=3^{2009}-3\)
Từ ( 1 ) và ( 2 ), ta có :
\(2A=3^{2009}-3\Leftrightarrow2A+3=3^{2009}\Rightarrow3^x=3^{2009}\Rightarrow x=2009\)
- Study well -
