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222-9+11+12:2*14+14 = ? ( )

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

Tháng Sáu 11, 2022 Toán học 1 Comment 0 views

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

Comments ( 1 )

  1. maianhtuanh
    maianhtuanh
    11 Tháng Sáu, 2022 at 3:30 chiều
    Reply
    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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222-9+11+12:2*14+14 = ? ( )

Khánh Giao

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