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

Toán Lớp 6: A=5 mũ 1 + 5 mũ 2 + 5 mũ 3 + 5 mũ 4 +…+ 5 mũ 240 (chứng minh A chia hết cho 31

Toán Lớp 6: A=5 mũ 1 + 5 mũ 2 + 5 mũ 3 + 5 mũ 4 +…+ 5 mũ 240 (chứng minh A chia hết cho 31

Comments ( 2 )

  1. $ A = 5 + 5^2+5^3+5^4+…+5^{240} $ 
    $ A = ( 5+5^2+5^3) + ( 5^4+5^5+5^6 ) + … + ( 5^{238} + 5^{239} + 5^{240} ) $ 
    $ A = 5 ( 1 + 5 + 5^2 ) + 5^4 ( 1+5+5^2 ) + …+ 5^{238} ( 1+5+5^2 ) $ 
    $ A = 5 . 31 + 5^4 . 31 + … + 5^{238} . 31 = ( 5+5^4+5^{238} ) . 31 $ 
    $ A  ⋮ 31 $

  2. A = 5 + $5^{1}$  + $5^{2}$  +…………+ $5^{240}$ 
    A = 1( 1+ 5 + $5^{2}$ )+…………..+$5^{238}$ (1+ 5 + $5^{2}$ )
    A = 1.31 +…………..+ $5^{238}$ .31
    A = 31.(1 +………….+ $5^{238}$ ) nên A chia hết cho 31.
    Chúc bạn học tốt~
     

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