Toán Lớp 7: CM A= 1/3 + 1/3^2 +1/3^3+…+1/3^2020 < 1/2

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Toán Lớp 7: CM A= 1/3 + 1/3^2 +1/3^3+…+1/3^2020 < 1/2, hướng dẫn giải giúp em bài này ạ, em cảm ơn thầy cô và các bạn nhiều.

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Khánh Giao 4 tuần 2022-06-11T15:28:52+00:00 1 Answer 0 views 0

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  1. Answer
    A = 1/3 + 1/3^{2} + 1/3^{3} + … + 1/3^{2020}
    1/3 . A = 1/3 . (1/3 + 1/3^{2} + 1/3^{3} + … + 1/3^{2020})
    1/3 . A = 1/3^{2} + 1/3^{3} + 1/3^{4} + … + 1/3^{2021}
    1/3 . A – A = (1/3^{2} + 1/3^{3} + 1/3^{4} + … + 1/3^{2021}) – (1/3 + 1/3^{2} + 1/3^{3} + … + 1/3^{2020})
    -2/3A = 1/3^{2021} – 1/3
    A = (1/3^{2021} – 1/3) : {-2}/3
    A = (1/3^{2021} – 1/3) . {-3}/2
    A = 1/3^{2021} . {-1}/2
    $\text{Vậy}$ A < 1/2
     

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