Question

cho A=3+3² +3³+........+3⁹⁹

chứng minh A chia hết cho 13

Answer 1

A=(3+3²+3³) + ......+(3⁹⁷+3⁹⁸+3⁹⁹)

A=3.(1+3+9)+.......+3⁹⁷(1+3+9)

A=3.13 + ...... +3⁹⁷.13

A=13.(3+......+3⁹⁷) chia hết cho 13 

Answer 2

A=(3+3²+3³) + ......+(3⁹⁷+3⁹⁸+3⁹⁹)

A=3.(1+3+9)+.......+3⁹⁷(1+3+9)

A=3.13 + ...... +3⁹⁷.13

A=13.(3+......+3⁹⁷) chia hết cho 13 

Answer 3

Ta có : 

\(A=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+...........+\left(3^{97}+3^{98}+3^{99}\right)\)\(\Rightarrow A=3.\left(1+3+3^2\right)+3^4.\left(1+3+3^2\right)+.............+3^{97}.\left(1+3+3^2\right)\)

\(\Rightarrow A=3.13+3^4.13+...............+3^{97}.13\)

=> \(\Rightarrow A=13.\left(3+3^4+.............+3^{94}+3^{97}\right)\)

Vậy A chia hết cho 3 ( đpcm)