Chứng minh rằng : A=2^1+2^2+2^3+2^4+…+2^2010 chia hết cho 3

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Chứng minh rằng : A=2^1+2^2+2^3+2^4+…+2^2010 chia hết cho 3

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Audrey 1 tháng 2021-08-04T20:38:54+00:00 2 Answers 1 views 0

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    2021-08-04T20:40:17+00:00

    *Hình dưới

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    2021-08-04T20:40:17+00:00

    Giải thích các bước giải:

    \(\begin{array}{l}A = {2^1} + {2^2} + {2^3} + {2^4} + … + {2^{2010}}\\A = \left( {{2^1} + {2^2}} \right) + \left( {{2^3} + {2^4}} \right) + … + \left( {{2^{2009}} + {2^{2010}}} \right)\\A = 2\left( {1 + 2} \right) + {2^3}\left( {1 + 2} \right) + … + {2^{2019}}\left( {1 + 2} \right)\\A = 2.3 + {2^3}.3 + … + {2^{2019}}.3\\A = \left( {2 + {2^3} + … + {2^{2019}}} \right).3\end{array}\)

    Vậy \(A\,\, \vdots \,\,3\).

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