Đáp án:
$\begin{array}{l}
2 + {2^2} + {2^3} + ... + {2^{100}}\\
= \left( {2 + {2^2}} \right) + \left( {{2^3} + {2^4}} \right) + ... + \left( {{2^{99}} + {2^{100}}} \right)\\
= 2\left( {1 + 2} \right) + {2^3}\left( {1 + 2} \right) + ... + {2^{99}}\left( {1 + 2} \right)\\
= 2.3 + {2^3}.3 + ... + {2^{99}}.3\\
= 3\left( {2 + {2^3} + ... + {2^{99}}} \right) \vdots 3
\end{array}$