2400

Ta có: \(B=3+3^2+\cdots+3^{20}\)

\(=\left(3+3^2\right)+\left(3^3+3^4\right)+\cdots+\left(3^{19}+3^{20}\right)\)

\(=\left(3+3^2\right)+3^2\left(3+3^2\right)+\cdots+3^{18}\left(3+3^2\right)\)

\(=12\left(1+3^2+\cdots+3^{18}\right)\) ⋮12

Đáp án cần chọn là: C

\(A=1+3+3^2+...+3^{11}\)

\(=\left(1+3\right)+\left(3^2+3^3\right)+...+\left(3^{10}+3^{11}\right)\)

\(=\left(1+3\right)+3^2\left(1+3\right)+...+3^{10}\left(1+3\right)\)

\(=4\left(1+3^2+...+3^{10}\right)⋮4\)

`#3107.101107`

`A = 1 + 3 + 3^2 + ... + 3^11`

`= (1 + 3) + (3^2 + 3^3) + ... + (3^10 + 3^11)`

`= (1 + 3) + 3^2(1 + 3) + ... + 3^10(1 + 3)`

`= (1 + 3)(1 + 3^2 + ... + 3^10)`

`= 4(1 + 3^2 + ... + 3^10)`

Vì `4(1 + 3^2 + ... + 3^10) \vdots 4`

`=> A \vdots 4.`

a, A =  5 + 5 2 + 5 3 + . . . + 5 8

= 5(1+5)+ 5 2 (1+5)+ 5 3 (1+5)+...+ 5 7 (1+5)

= 30+5.30+ 5 2 .30+...+ 5 6 .30

= 30.(1+5+ 5 2 +..+ 5 6 )

Vậy A là bội của 30

b, B =  3 + 3 3 + 3 5 + 3 7 + . . . + 3 29

= 3 1 + 3 2 + 3 4 + 3 7 1 + 3 2 + 3 4 +...+ 3 27 1 + 3 2 + 3 4

= 273+273. 3 6 +...+ 3 26 .273

= 273.(1+ 3 6 +...+ 3 26 )

Vậy B là bội của 273