1/ \(3+3^2+3^3+...+3^{99}\)
\(=\left(3+3^2\right)+\left(3^3+3^4\right)+...\left(3^{98}+3^{99}\right)\)
\(=1\left(3+3^2\right)+3^2\left(3+3^2\right)+...+3^{97}\left(3+3^2\right)\)
\(=12\left(1+3^2+...+3^{97}\right)⋮12^{\left(đpcm\right)}\)
1.
\(3+3^2+3^3+...+3^{99}\)
\(=\left(3+3^2+3^3\right)+...+\left(3^{97}+3^{98}+3^{99}\right)\)
\(=3\left(1+3+9\right)+...+3^{97}\left(1+3+9\right)\)
\(=16\left(3+3^4+...+3^{97}\right)\)
VÌ \(\hept{\begin{cases}16⋮4\\3+3^4+...+3^{97}⋮3\end{cases}}\)
VẬY \(3+3^2+3^3+...+3^{99}\)\(⋮\)12