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

Toán Lớp 7: Cho `B=1/2^3+1/3^3+1/4^3+…+1/2021^3`. CMR `B<1/2^2`

Tháng Bảy 12, 2022 Toán học 1 Comment 0 views

Toán Lớp 7: Cho B=1/2^3+1/3^3+1/4^3+…+1/2021^3. CMR B<1/2^2

Comments ( 1 )

  1. hienthucthu97
    hienthucthu97
    12 Tháng Bảy, 2022 at 2:18 chiều
    Reply
    Giải đáp + Lời giải và giải thích chi tiết:
    B=1/2^3+1/3^3+1/4^3+…+1/2021^3
    =>B<1/(1.2.3)+1/(2.3.4)+1/(3.4.5)+…1/(2020.2021.2022)
    =>B<1/2(2/(1.2.3)+2/(2.3.4)+2/(3.4.5)+…+2/(2020.2021.2022))
    =>B<1/2(1/1.2-1/2.3+1/2.3-1/3.4+1/3.4-1/4.5+…+1/2020.2021-1/2021.2022)
    =>B<1/2(1/1.2-1/2021.2022)
    =>B<1/2(1/2-1/2021.2022)
    =>B<1/2^2-1/(2.2021.2022)<1/2^2
    Vậy B<1/2^2
     

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

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