chứng minh rằng 1^(2+2+2^(2+2^(3+…+2^(99+2^(100=2^(101-1

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chứng minh rằng 1^(2+2+2^(2+2^(3+…+2^(99+2^(100=2^(101-1

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Maria 1 tháng 2021-08-03T23:02:22+00:00 1 Answers 1 views 0

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    2021-08-03T23:03:41+00:00

    Đáp án:

    $\begin{array}{l}
    A = 1 + 2 + {2^2} + {2^3} + … + {2^{99}} + {2^{100}}\\
     \Rightarrow 2.A = 2\left( {1 + 2 + {2^2} + {2^3} + … + {2^{99}} + {2^{100}}} \right)\\
     \Rightarrow 2A = 2 + {2^2} + {2^3} + … + {2^{100}} + {2^{101}}\\
     \Rightarrow 2A – A = \left( {2 + {2^2} + {2^3} + … + {2^{100}} + {2^{101}}} \right) – \\
    \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {1 + 2 + {2^2} + {2^3} + … + {2^{99}} + {2^{100}}} \right)\\
     \Rightarrow A = {2^{101}} – 1
    \end{array}$

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