Chứng minh: $\mathbf{A}=2^{1}+2^{2}+2^{3}+2^{4}+\ldots+2^{2010}$ chia hết cho 3

Q: Chứng minh: $\mathbf{A}=2^{1}+2^{2}+2^{3}+2^{4}+\ldots+2^{2010}$ chia hết cho 3

<span class="math-tex">$\begin{array}{l}\mathbf{A}=2^{1}+2^{2}+2^{3}+2^{4}+\ldots+2^{2020} \\\mathrm{~A}=2 \cdot(1+2)+2^{3} \cdot(1+2)+\ldots 2^{2019} \cdot(1+2) \\\mathrm{A}=2 \cdot 3+2^{3} \cdot 3+\ldots 2^{2019} \cdot 3 \\\mathrm{~A}=\left(2+2^{3}+\ldots 2^{2019}\right) \cdot 3\end{array}$</span><p>Vì 3 chia hết cho 3 nên A chia hết cho 3</p>

Question

Accepted Answer

$\begin{array}{l}\mathbf{A}=2^{1}+2^{2}+2^{3}+2^{4}+\ldots+2^{2020} \\mathrm{~A}=2 \cdot(1+2)+2^{3} \cdot(1+2)+\ldots 2^{2019} \cdot(1+2) \\mathrm{A}=2 \cdot 3+2^{3} \cdot 3+\ldots 2^{2019} \cdot 3 \\mathrm{~A}=\left(2+2^{3}+\ldots 2^{2019}\right) \cdot 3\end{array}$

Vì 3 chia hết cho 3 nên A chia hết cho 3

Đề thi cuối kì 1 (CT) 19-20 - Q.10 - Tp. Hồ Chí Minh - MĐ 6314