S=1+22+23+...+22020
2S= 22+23+24+...+22021
2S - S = S = (22- 22) + (23-23)+ (24- 24)+...+(22020-22020) + (22021-1)
= 22021 - 1
\(S=1+2^2+2^3+...+2^{2020}\)
\(=1+\left(2^2+2^3+...+2^{2020}\right)\). Đặt:
\(A=2^2+2^3+...+2^{2020}\Rightarrow2A=2^3+2^4+...+2^{2021}\)
Do 2A - A = A nên \(A=\left(2^3+2^4+...+2^{2021}\right)-\left(2^2+2^3+...+2^{2020}\right)\)
\(A=2^{2021}-2^2\Rightarrow S=1+\left(2^{2021}-2^2\right)=1+2^{2021}-4\)
Vậy: \(S=1+2^{2021}-4\)
Thêm tí xíu,chỗ:
Vậy: \(S=1+2^{2021}-4=2^{2021}-4+1=2^{2021}-\left(4-1\right)=2^{2021}-3\)
