Cho A = 3+3^2+3^3+3^4+………+3^25 Tìm số dư khi chia A cho 40 24/08/2021 Bởi aihong Cho A = 3+3^2+3^3+3^4+………+3^25 Tìm số dư khi chia A cho 40
Đáp án: $\begin{array}{l}A = 3 + {3^2} + {3^3} + {3^4} + … + {3^{25}}\\ = 3 + \left( {{3^2} + {3^3} + {3^4} + {3^5}} \right) + …. + \left( {{3^{22}} + {3^{23}} + {3^{24}} + {3^{25}}} \right)\\ = 3 + 3\left( {1 + 3 + {3^2} + {3^3}} \right) + … + {3^{22}}\left( {1 + 3 + {3^2} + {3^3}} \right)\\ = 3 + 3.40 + … + {3^{22}}.40\\ = 3 + 40\left( {3 + {3^6} + … + {3^{22}}} \right)\\Do:\,40\left( {3 + {3^6} + … + {3^{22}}} \right) \vdots 40\\ \Rightarrow 40\left( {3 + {3^6} + … + {3^{22}}} \right) + 3\,\,\,chia\,40\,\,dư\,\,3\end{array}$ Bình luận
Đáp án:
$\begin{array}{l}
A = 3 + {3^2} + {3^3} + {3^4} + … + {3^{25}}\\
= 3 + \left( {{3^2} + {3^3} + {3^4} + {3^5}} \right) + …. + \left( {{3^{22}} + {3^{23}} + {3^{24}} + {3^{25}}} \right)\\
= 3 + 3\left( {1 + 3 + {3^2} + {3^3}} \right) + … + {3^{22}}\left( {1 + 3 + {3^2} + {3^3}} \right)\\
= 3 + 3.40 + … + {3^{22}}.40\\
= 3 + 40\left( {3 + {3^6} + … + {3^{22}}} \right)\\
Do:\,40\left( {3 + {3^6} + … + {3^{22}}} \right) \vdots 40\\
\Rightarrow 40\left( {3 + {3^6} + … + {3^{22}}} \right) + 3\,\,\,chia\,40\,\,dư\,\,3
\end{array}$
Đáp án:
du 3