Question

Không thực hiện phép tính , hãy so sánh:

A=2¹+2²+...+2¹⁰ và B=2¹¹

Answer 1

Ta có

\(2A=2^2+2^3+.....+2^{11}\)

\(\Rightarrow2A-A=\left(2^2+2^3+.....+2^{11}\right)-\left(2+2^2+....+2^{10}\right)\)

\(\Rightarrow A=2^{11}-2< 2^{11}\)

=> A<2^11

Answer 2

\(Tac\text{ó}:\\ 2A=2^2+2^3+..........+2^{11}\\ =2A-A=\left(2^2+2^3+......+2^{11}\right)-\left(2+2^2+....+2^{10}\right)\\ =>A=2^{11}-2< 2^{11}\\ =>A< 2^{11}\)