Question

Cho A=1+3+3 mũ 2+3 mũ 3+3 mũ 4+3 mũ 5+...+3 mũ 2018+3 mũ 2019+3 mũ 2020

Answer 1

\(A=1+3+3^2+...+3^{2020}\)  \(\Rightarrow3A=3+3^2+3^3+...+3^{2021}\)

\(\Rightarrow2A=3^{2021}-1\)  \(\Rightarrow A=\dfrac{3^{2021}-1}{2}\)

Answer 2

`A  = 1 + 3 + 3^2 + 3^3 + ... + 3^2020`

`=> 3A = 3 + 3^2 + 3^3 + 3^4 + ... + 3^2021`

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

`=> 2A = 3^2021 - 1`

`=> A    = (3^2021-1)/2`