Question

Cho biểu thức A = 1 + 2¹ + 2¹+ 2² + 2³ + .... + 2²⁰²¹

Tìm x ∈ N sao cho 2^x = A + 1

Answer 1

Sửa: \(A=1+2^1+2^2+2^3+...+2^{2021}\)

\(\Rightarrow A+1=1+1+2+2^2+...+2^{2021}\\ \Rightarrow A+1=2+2+2^2+...+2^{2021}\\ \Rightarrow A+1=2^2+2^2+2^3+...+2^{2021}\\ \Rightarrow A+1=2^3+2^3+2^4+...+2^{2021}\\ ....\\ \Rightarrow A+1=2^{2021}+2^{2021}=2^{2022}\)

Mà \(2^x=A+1\Rightarrow2^x=2^{2022}\Rightarrow x=2022\)

Answer 2

\(A=1+2^1+2^1+2^2+...+2^{2021}\\ \Rightarrow A=1+2+2+2^2+...+2^{2021}\\ \Rightarrow A=1+2.2+2^2+...+2^{2021}\\ \Rightarrow A=1+2^2+2^2+...+2^{2021}\\ \Rightarrow A=1+2.2^2+...+2^{2021}\\ \Rightarrow A=1+2^3+...+2^{2021}\)

....

\(\Rightarrow A=1+2^{2022}\)

\(2^x=1+A\\ \Rightarrow2^x=1+1+2^{2022}\\ \Rightarrow2^x=2+2^{2022}\)

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