Đáp án:
$\begin{array}{l}
a)S = 3 + {3^2} + {3^3} + ... + {3^{100}}\\
\Rightarrow 3.S = {3^2} + {3^3} + {3^4} + ... + {3^{101}}\\
\Rightarrow 3S - S = 2S = {3^{101}} - 3\\
\Rightarrow 2S + 3 = {3^{101}} - 3 + 3 = {3^{101}}\\
\Rightarrow 2S + 3\,\text{là lũy thừa của 3}\\
b)A = 2 + {2^2} + {2^3} + ... + {2^{10}}\\
= \left( {2 + {2^2}} \right) + \left( {{2^3} + {2^4}} \right) + ... + \left( {{2^9} + {2^{10}}} \right)\\
= 2.\left( {1 + 2} \right) + {2^3}\left( {1 + 2} \right) + ... + {2^9}.\left( {1 + 2} \right)\\
= 2.3 + {2^3}.3 + ... + {2^9}.3\\
= \left( {2 + {2^3} + ... + {2^9}} \right).3 \vdots 3\\
\text{Vậy}\,A \vdots 3
\end{array}$
