a) chung minh 5+5^2+5^3+…+5^2020=3^2020-5/4

Question

a) chung minh 5+5^2+5^3+…+5^2020=3^2020-5/4

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Farah 4 years 2020-11-24T15:41:45+00:00 1 Answers 50 views 0

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  1. Eirian
    0
    2020-11-24T15:43:29+00:00
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    Bạn tham khảo :

    Đặt $A = 5 + 5^2 + 5^3 +… + 5^{2020}$

    ⇒ $5^2A = 5^2 + 5^3 + 5^4 + … + 5^{2020}$

    ⇒ $5^2A -A = ( 5^2 + 5^3 + 5^4 + … + 5^{2022}) – ( 5+ 5^2 + 5^3+ … + 5^{2020})$

    ⇒ $24A = 5^{2022} – 5$

    ⇒ $A = \dfrac{5^{2022}} – {5}{24}$  

    ⇒ $A = \dfrac{5^{2022} . 24 – 5}{24}$

    ⇒ $A = \dfrac{5^2022. 23}{24}$

    Ta có :

    $3^{2020} – \dfrac{5}{4} = \dfrac{3^{2020}.4}{4} – \dfrac{5}{4} = \dfrac{3^{2020} – 5}{4}=\dfrac{3^{2020} – 5 . 6}{24}= \dfrac{3^{2020} – 30}{24}$

    Đến đây tịt rồi @@ 

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