Question

Tính hợp lí: 1 + 2 + 2² + 2³ + 2⁴ + ... 2⁹⁹ + 2¹⁰⁰

 

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Answer 1

\(A=1+2+2^2+2^3+2^4+...+2^{99}+2^{100}\)

\(\Rightarrow2A=2+2^2+2^3+2^4+2^5+...+2^{100}+2^{101}\)

\(\Rightarrow2A-A=2^{101}-1\)

\(\Leftrightarrow A=2^{101}-1\)

Answer 2

Đặt biểu thức là A

ta có 2A-A=2^101-1

Answer 3

Đặt \(A=1+2+2^2+2^3+2^4+...+2^{99}+2^{100}\)

\(\Rightarrow2A=2+2^2+2^3+...+2^{100}+2^{101}\)

\(\Rightarrow A=2A-A=\left(2+2^2+2^3+2^4+...+2^{101}\right)-\left(1+2+2^2+2^3+...+2^{100}\right)=2^{101}-1\)

Answer 4

Ta có: \(A=1+2+2^2+...+2^{100}\)

\(\Leftrightarrow2\cdot A=2+2^2+2^3+...+2^{100}+2^{101}\)

\(\Leftrightarrow A=2^{101}-1\)