Đáp án:
$\begin{array}{l}
{3^1} + {3^2} + {3^3} + .. + {3^{2018}} + {3^{2019}}\\
= \left( {3 + {3^2} + {3^3}} \right) + \left( {{3^4} + {3^5} + {3^6}} \right) + ... + \left( {{3^{2017}} + {3^{2018}} + {3^{2019}}} \right)\\
= 3\left( {1 + 3 + {3^2}} \right) + {3^4}\left( {1 + 3 + {3^2}} \right) + ... + {3^{2017}}\left( {1 + 3 + {3^2}} \right)\\
= 3.13 + {3^4}.13 + ... + {3^{2017}}.13\\
= 13\left( {3 + {3^4} + .. + {3^{2017}}} \right) \vdots 13\\
\Rightarrow dieu\,phai\,chung\min h
\end{array}$