a=5+4^2+4^3+….+4^2021. CMR 3a+1 chia hết cho 4^2021

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a=5+4^2+4^3+….+4^2021. CMR 3a+1 chia hết cho 4^2021

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Thu Cúc 5 years 2021-05-18T07:33:03+00:00 1 Answers 29 views 0

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  1. Thunguyet
    0
    2021-05-18T07:34:08+00:00
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    `a = 5 + 4^2 + 4^3 + … + 4^2021`

    `= 1 + 4 + 4^2 + 2^3 + … + 4^2021`

    ⇒ `4a = 4 + 4^2 + 4^3 + 4^4 + … + 4^2022`

    ⇒ `4a – a = (4 + 4^2 + 4^3 + 4^4 + … + 4^2022) – (1 + 4 + 4^2 + 2^3 + … + 4^2021)`

    ⇒ `3a = 4^2022 – 1`

    ⇒ `3a + 1 = 4^2022 – 1 + 1 = 4^2022 = 4^2021 . 4 \vdots 4^2021` `(đpcm)`

    Vậy…

     

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