Question

\(A=1+2+2^2+2^3+...+2^{2021}\)

Answer 1

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

`2A=2+2^2+2^3+....+2^2022`

`=>2A-A=A=2^2022-1`

Answer 2

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

`=> 2A = 2.(1 + 2  + 2^2 + 2^3 + ... + 2^2021)`

`=> 2A = 2 + 2^2 + 2^3 + 2^4 + ... + 2^2022`

`-`

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

`=> A = 2^2022 - 1`

Vậy `A = 2^2022 - 1`