1+2+2^2+2^3+2^4+2^5+……+2^2017 Tìm số tự nhiên n,biết 2.(A+1)=2^n+1

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1+2+2^2+2^3+2^4+2^5+……+2^2017
Tìm số tự nhiên n,biết 2.(A+1)=2^n+1

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Iris 3 tuần 2021-11-25T19:37:38+00:00 1 Answers 1 views 0

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    2021-11-25T19:39:35+00:00

    Đặt N = 1 + 2 + 2^2 + 2^3+2^4+2^5+….+2+2017

    ⇒2N = 2 ( 1+2+2^2+2^3+2^4+2^5+……+2^2017)

      2N= 2+ 2^2+2^3+2^4+2^5+2^6+……+2^2018

    ⇒2N-N=(2+2^2+2^3+2^4+2^5+2^6+…….+2^2018) – ( 1+ 2+2^2+2^3+2^4+2^5+……..+2^2017)

                 = 2^2018 – 1 

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