Question

Cho

A= 2^0+2^1+2^2+2^3+....+ 2^50

B= 2^51

So sánh A và B

Answer 1

Ta có: \(A=2^0+2^1+2^2+2^3+...+2^{50}\)

\(\Rightarrow2A=2\left(2^0+2^1+2^2+2^3+...+2^{50}\right)\)

\(\Rightarrow2A=2+2^2+2^3+2^4+...+2^{51}\)

\(\Rightarrow2A-A=\left(2+2^2+2^3+2^4+...+2^{51}\right)-\left(2^0+2+2^2+2^3+...+2^{50}\right)\)

\(\Rightarrow A=2^{51}-1\) \(< 2^{51}\)

\(\Rightarrow A< B\)

Answer 2

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 : \(2^{51}-1< 2^{51}\Rightarrow A< B\)

Answer 3

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!

Answer 4

\(A=2^0+2^1+2^2+2^3+.........+2^{50}\)

\(A=1+2+2^2+2^3+........+2^{50}\)

\(2A=2\left(1+2+2^2+2^3+........+2^{50}\right)\)

\(2A=2+2^2+2^3+2^4+........+2^{51}\)

\(2A-A=\left(2+2^2+2^3+2^4+........+2^{51}\right)-\left(1+2+2^2+2^3+..........+2^{50}\right)\)\(A=2^{51}-1\)

\(A< 2^{51}\Leftrightarrow A< B\)

Answer 5

\(A=2^0+2^1+2^2+2^3+...+2^{50}\)

\(A=1+2+2^2+2^3+...+2^{50}\)

\(2A=2+2^2+2^3+...+2^{51}\)

\(2A-A=2^{51}-1\)

Ta thấy: \(2^{51}-1< 2^{51}\)

\(\Rightarrow A< B\)

Vậy A<B