Ta có :
\(A=1+3+3^2+...................+3^{10}\)
\(\Leftrightarrow3A=3+3^2+..................+3^{10}+3^{11}\)
\(\Leftrightarrow3A-A=\left(3+3^2+.............+3^{11}\right)-\left(1+3+.................+3^{10}\right)\)
\(\Leftrightarrow2A=3^{11}-1\)
\(\Leftrightarrow2A+1=3^{11}\)
\(\Leftrightarrow3^{11}=3^n\)
\(\Leftrightarrow n=11\left(TM\right)\)
Vậy \(n=11\) là giá trị cần tìm
\(A=1+3+3^2+3^3+...+3^{10}\)
\(3A=3\left(1+3+3^2+3^3+...+3^{10}\right)\)
\(3A=3+3^2+3^3+3^4+...+3^{11}\)
\(A=1+3+3^2+3^3+...+3^{10}\)
\(2A=3^{11}-1\)
\(2A+1=3^{11}\)
Mà \(2A+1=3^n\)
\(\Rightarrow\) n = 11
Vậy n = 11
