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

Toán Lớp 6: Chứng minh rằng S chia hết cho 2;5 S=2+2^2+2^3+2^4+…+2^99+2^100

Toán Lớp 6: Chứng minh rằng S chia hết cho 2;5
S=2+2^2+2^3+2^4+…+2^99+2^100

Comments ( 2 )

  1. Giải đáp+Lời giải và giải thích chi tiết:
    S=2+2^2+2^3+2^4+…+2^99+2^100
    S=1.2+2.2+2. 2^2+2. 2^3+…+2. 2^98+2. 2^99
    S=2(1+2+2^2+2^3+…+2^98+2^99)\vdots2
    ———————————————–
    S=2+2^2+2^3+2^4+…+2^99+2^100
    S=(2+2^3)+(2^2+2^4)+…+(2^97+2^99)+(2^98+2^100)
    S=2(1+4)+2^2(1+4)+…+2^97(1+4)+2^98(1+4)
    S=2.5+2^2. 5+…+2^97. 5+2^98. 5
    S=5(2+2^2+…+2^97+2^98)\vdots5

  2. Giải thích:
    -> Chứng minh S $\vdots$ 2:
    S = 2 + 2² + 2³ + 2⁴ +…….+ 2⁹⁹ + 2¹⁰⁰.
    S = 1×2 + 2×2 + 2×2² + 2×2³ +………+ 2×2⁹⁸ + 2×2⁹⁹.
    S = 2( 1+ 2 + 2² + 2³ +………+ 2⁹⁸ + 2⁹⁹ ) $\vdots$ 2
    -> S $\vdots$ 2
    -> Chứng minh S $\vdots$ 5:
    S = 2 + 2² + 2³ + 2⁴ +……….+ 2⁹⁹ + 2¹⁰⁰.
    S = ( 2 + 2³ ) + ( 2² + 2⁴ ) +………+ ( 2⁹⁷ + 2⁹⁹ ) + ( 2⁹⁸ + 2¹⁰⁰ )
    S = 2( 1 + 4 ) + 2²( 1 + 4 ) +………..+ 2⁹⁷( 1 + 4 ) + 2⁹⁸( 1 + 4 ).
    S = 2 × 5 + 2² × 5 + 2³ × 5 +………….+ 2⁹⁷ × 5 + 2⁹⁸ × 5.
    S = 5( 2 + 2² + 2³ +………….+ 2⁹⁷ + 2⁹⁸ ) $\vdots$ 5
    -> S $\vdots$ 5
     

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