Toán chứng minh rằng 1^(2+2+2^(2+2^(3+…+2^(99+2^(100=2^(101-1 03/08/2021 By Maria chứng minh rằng 1^(2+2+2^(2+2^(3+…+2^(99+2^(100=2^(101-1
Đáp án: $\begin{array}{l}A = 1 + 2 + {2^2} + {2^3} + … + {2^{99}} + {2^{100}}\\ \Rightarrow 2.A = 2\left( {1 + 2 + {2^2} + {2^3} + … + {2^{99}} + {2^{100}}} \right)\\ \Rightarrow 2A = 2 + {2^2} + {2^3} + … + {2^{100}} + {2^{101}}\\ \Rightarrow 2A – A = \left( {2 + {2^2} + {2^3} + … + {2^{100}} + {2^{101}}} \right) – \\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {1 + 2 + {2^2} + {2^3} + … + {2^{99}} + {2^{100}}} \right)\\ \Rightarrow A = {2^{101}} – 1\end{array}$ Trả lời
Đáp án:
$\begin{array}{l}
A = 1 + 2 + {2^2} + {2^3} + … + {2^{99}} + {2^{100}}\\
\Rightarrow 2.A = 2\left( {1 + 2 + {2^2} + {2^3} + … + {2^{99}} + {2^{100}}} \right)\\
\Rightarrow 2A = 2 + {2^2} + {2^3} + … + {2^{100}} + {2^{101}}\\
\Rightarrow 2A – A = \left( {2 + {2^2} + {2^3} + … + {2^{100}} + {2^{101}}} \right) – \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {1 + 2 + {2^2} + {2^3} + … + {2^{99}} + {2^{100}}} \right)\\
\Rightarrow A = {2^{101}} – 1
\end{array}$