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

Toán Lớp 7: A= 1/4+1/4^2+1/4^3+1/4^4+-+1/4^2020 < 1/3

Home/ Toán Lớp 7: A= 1/4+1/4^2+1/4^3+1/4^4+-+1/4^2020 < 1/3

Toán Lớp 7: A= 1/4+1/4^2+1/4^3+1/4^4+-+1/4^2020 < 1/3

Tháng Tám 30, 2022 Toán học 2 Comments 0 views

Toán Lớp 7: A= 1/4+1/4^2+1/4^3+1/4^4+….+1/4^2020 < 1/3

Comments ( 2 )

  1. bichhhathu
    bichhhathu
    30 Tháng Tám, 2022 at 7:52 sáng
    Reply
    Giải đáp:
    A<1/3
    Lời giải và giải thích chi tiết:
    A=1/4+1/4^2+….+1/4^2020
    1/4A=1/4^2+1/4^3+…+1/4^2021
    1/4A-A=(1/4^2+1/4^3+…+1/4^2021)-(1/4+1/4^2+….+1/4^2020)
    (-3)/4A=1/4^2021-1/4
    A=(1/4^2021-1/4)\times(-4)/3
    =>A<1/3 (Vì A âm)
    Vậy A<1/3

  2. lanhuongthu
    lanhuongthu
    30 Tháng Tám, 2022 at 7:51 sáng
    Reply
    A=1/4+1/(4^2)+1/(4^3)+1/(4^4)+…+1/(4^2020)
    =>1/4 .A=1/(4^2)+1/(4^3)+1/(4^4)+1/(4^5)+…+1/(4^2021)
    =>1/4A-A=(1/(4^2)+1/(4^3)+1/(4^4)+1/(4^5)+…+1/(4^2021))-(1/4+1/(4^2)+1/(4^3)+1/(4^4)+…+1/(4^2020))
    =>A=(1/(4^2021)-1/4).(-4)/3
    =>A luôn âm
    =>A<1/3
     

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

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