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

Toán Lớp 6: cho A= 1+3+3 mũ 2+3 mũ 3+…+3 mũ 100.Chứng minh A chia hết cho 13

Toán Lớp 6: cho A= 1+3+3 mũ 2+3 mũ 3+…+3 mũ 100.Chứng minh A chia hết cho 13

Comments ( 2 )

  1. A=1+3+3²+3³+….+$3^{100}$ 
    =(1+3+3²)+(3³+$3^{4}$+$3^{5}$ )+….+($3^{98}$+$3^{99}$ +$3^{100}$ 
    =1.13+3³.13+….+$3^{98}$.13
    =[13.(1+3³+…+$3^{98}$)]⋮13
    Vậy A⋮13

  2. A =1+3+3^2+3^3 + … +3^100
    => A = (1+3+3^2) + (3^3+3^4+3^5) + … + (3^98 + 3^99 +3^100)
    => A = 13 + 3^3 (1+3+3^2) + … +3^98 (1+3+3^2)
    => A = 13 +3^3 . 13 + … +3^98 .13
    => A = 13(1+3^3+ … +3^98) \vdots 13 (đpcm).
    Vậy A \vdots 13. 

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