Question

2 +2 mũ 2 + 2 mũ 3 +...+2 mũ 100 chia hết cho 6 không ? vì sao?

Answer 1

\(\text{#ID07 - DNfil}\)

Đặt `A = 2 + 2^2 + 2^3 + ... + 2^100`

Ta có:

`A = (2 + 2^2) + (2^3 + 2^4) + ... + (2^99 + 2^100)`

`= (2 + 2^2) + 2^2 (2 + 2^2) + ... + 2^98 (2 + 2^2)`

`= (2 + 2^2)(1 + 2^2 + ... + 2^98)`

`= 6(1 + 2^2 + ... + 2^98)`

Vì `6(1 + 2^2 + ... + 2^98) \vdots 6`

`=> A \vdots 6`

Vậy, `A \vdots 6.`