Question

Chứng tỏ : 1+2 mũ 1 + 2 mũ 2 + 2 mũ 3 +..... + 2 mũ 2021 chia hết cho 3

giúp mik nha

Answer 1

`A  = 1 + 2 + 2^2(1+2) + ... + 2^2020(1+2)`

`= 3 + 2^2 .3 + ... + 2^2020.3`

`= 3(1+2^2+...+2^2020) vdots3.`

Answer 2

`1+2^1 + 2^2 + 2^3 + ... + 2^2021`

`= (1+2^1) + (2^2 + 2^3) + ... + (2^2020 + 2^2021)`

`= 3 + 2^2 . (1+2) + ... + 2^2020 . (1+2)`

`= 3 + 2^2 . 3 + ... + 2^2020 . 3`

`= 3.(1 + 2^2 + ... + 2^2020) \vdots 3`