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

Toán Lớp 7: chứng minh A=1/3+1/3^2+1/3^3+…+1/3^2021<1/2

Home/ Toán Lớp 7: chứng minh A=1/3+1/3^2+1/3^3+…+1/3^2021<1/2

Toán Lớp 7: chứng minh A=1/3+1/3^2+1/3^3+…+1/3^2021<1/2

Tháng Bảy 23, 2022 Toán học 1 Comment 0 views

Toán Lớp 7: chứng minh A=1/3+1/3^2+1/3^3+…+1/3^2021<1/2

Comments ( 1 )

  1. thanhtung
    thanhtung
    23 Tháng Bảy, 2022 at 3:13 sáng
    Reply
     A = $\frac{1}{3}$ + $\frac{1}{3^2}$ + … + $\frac{1}{3^{99} }$ 
    3A = 3 ( $\frac{1}{3}$ + $\frac{1}{3^2}$ + … + $\frac{1}{3^{99} }$ ) 
    3A = 1 + $\frac{1}{3}$ + $\frac{1}{3^2}$ + … + $\frac{1}{3^{98} }$
    3A – A = ( 1 + $\frac{1}{3}$ + $\frac{1}{3^2}$ + … + $\frac{1}{3^{98} }$ ) – ( $\frac{1}{3}$ + $\frac{1}{3^2}$ + … + $\frac{1}{3^{99} }$ ) 
    2A = 1 – $\frac{1}{3^{99} }$ 
    A = $\frac{1-\frac{1}{3^{99}} }{2}$ 
    ⇒ A < $\frac{1}{2}$ 

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

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