Ta có: \(A=2^0+2^1+2^2+2^3+...+2^{50}\)
\(\Rightarrow2A=2\left(2^0+2^1+2^2+2^3+...+2^{50}\right)\)
\(\Rightarrow2A=2+2^2+2^3+2^4+...+2^{51}\)
\(\Rightarrow2A-A=\left(2+2^2+2^3+2^4+...+2^{51}\right)-\left(2^0+2+2^2+2^3+...+2^{50}\right)\)
\(\Rightarrow A=2^{51}-1\) \(< 2^{51}\)
\(\Rightarrow A< B\)
Ta có :\(A= 2^0+2^1+2^2+2^3+....+ \) \(2^{50}\)
\(2A= 2^1+2^2+2^3+2^4+....+\) \(2^{51}\)
\(2A-A=\left(2^1+2^2+...+2^{51}\right)-\left(2^0+2^1+...+2^{50}\right)\\ A=2^{51}-1\)
Ta có : \(2^{51}-1< 2^{51}\Rightarrow A< B\)
Giải:
Có:
\(A=2^0+2^1+2^2+2^3+...+2^{50}\)
\(\Rightarrow2A=2^1+2^2+2^3+2^4+...+2^{51}\)
\(\Leftrightarrow2A-A=\left(2^1+2^2+2^3+2^4+...+2^{51}\right)-\left(2^0+2^1+2^2+2^3+...+2^{50}\right)\)
\(\Leftrightarrow A=2^1+2^2+2^3+2^4+...+2^{51}-2^0-2^1-2^2-2^3-...-2^{50}\)
\(\Leftrightarrow A=2^{51}-2^0=2^{51}-1\)
Mà \(2^{51}-1< 2^{51}\)
\(\Leftrightarrow A< B\)
Vậy \(A< B\)
Chúc bạn học tốt!
\(A=2^0+2^1+2^2+2^3+.........+2^{50}\)
\(A=1+2+2^2+2^3+........+2^{50}\)
\(2A=2\left(1+2+2^2+2^3+........+2^{50}\right)\)
\(2A=2+2^2+2^3+2^4+........+2^{51}\)
\(2A-A=\left(2+2^2+2^3+2^4+........+2^{51}\right)-\left(1+2+2^2+2^3+..........+2^{50}\right)\)\(A=2^{51}-1\)
\(A< 2^{51}\Leftrightarrow A< B\)
\(A=2^0+2^1+2^2+2^3+...+2^{50}\)
\(A=1+2+2^2+2^3+...+2^{50}\)
\(2A=2+2^2+2^3+...+2^{51}\)
\(2A-A=2^{51}-1\)
Ta thấy: \(2^{51}-1< 2^{51}\)
\(\Rightarrow A< B\)
Vậy A<B