\(A=3+3^2+3^3+...+3^{100}\)
\(\Rightarrow3A=3^2+3^3+3^4+...+3^{101}\)
\(\Rightarrow3A-A=\left(3^2+3^3+3^4+...+3^{101}\right)-\left(3+3^2+3^3+...+3^{100}\right)\)
\(\Rightarrow2A=3^{101}-3\)
Mà \(2A+3=3^n\)
\(\Rightarrow3^{101}-3+3=3^n\)
\(\Rightarrow3^n=3^{101}\)
\(\Rightarrow n=101\)
Vậy n = 101
A = 3 + 32 + 33 + ... + 3100
=> 3A= 32 + 33 + ... + 3101
=> 3A-A=( 32 + 33 + ... + 3101)-(3 + 32 + 33 + ... + 3100)
=> 2A=3101-3
Mà : 2A+3=3n
=> \(3^{101}-3+3=3^n\)
\(\Rightarrow3^{101}=3^n\)
=> n=101
em làm đúng sao thầy ko tích nhỉ ?? phynit
