Question

[Trần Đan Thi]

 cho A= 1+2+2 mũ 2+2 mũ3+...+2 mũ 2018 và B= 2 mũ2019+ 1. so sánh A và B

Answer 1

[Nguyệt]

\(2A=2.\left(1+2+2^2+...+2^{2018}\right)\)

\(2A=2+2^2+...+2^{2019}\)

\(2A-A=2+2^2+...+2^{2019}-\left(1+2+...+2^{2018}\right)\)

\(A=2^{2019}-1< 2^{2019}< 2^{2019}+1\)

\(=>A< B\)

Answer 2

[Đoàn Đức Hà]

\(A=1+2+2^2+...+2^{2018}\)

\(2A=2+2^2+2^3+...+2^{2019}\)

\(2A-A=\left(2+2^2+2^3+...+2^{2019}\right)-\left(1+2+2^2+...+2^{2018}\right)\)

\(A=2^{2019}-1\)

Suy ra \(A< B\).