Question

B = 1 + 3 + 3² + 3³ + ... + 3⁹⁸ + 3⁹⁹

^{CMR: B chia hết cho 4}

^{Ai nhanh mình tick cho}

Answer 1

Ta có: B=(1+3)+(3²+3³)+..........+(3⁹⁸+3⁹⁹)

=> B=1.(1+3)+3².(1+3)+............+3⁹⁸.(1+3)

=> B=1.4+3².4+.......+3⁹⁸.4

=> B=4.(1+3²+..........+3⁹⁸)

Vậy B chia hết cho 4                        ĐPCM

Answer 2

\(B=1+3+3^2+3^3+...+3^{98}+3^{99}\)

=> \(B=\left(1+3\right)+\left(3^2+3^3\right)+\left(3^4+3^5\right)+...+\left(3^{98}+3^{99}\right)\)

=> \(B=4+3^2\left(1+3\right)+3^4\left(1+3\right)+...+3^{98}\left(1+3\right)\)

=> \(B=4+3^3.4+3^4.4+...+3^{98}.4\)

=> \(B=4\left(3^2+3^4+...+3^{98}\right)\)

Vì 4 chia hết cho 4 => \(4\left(3^2+3^4+...+3^{98}\right)\) chia hết cho 4 => B chia hết cho 4