Question

Cho A= 1 + 2 + 2^2 + … + 2^2002 và B = 2^2003 – 1. So sánh A và B

Answer 1

\(\Rightarrow2A=2+2^2+2^3+...+2^{2003}\\ \Rightarrow2A-A=2+2^2+2^3+...+2^{2003}-1-2-...-2^{2002}\\ \Rightarrow A=2^{2003}-1=B\)

Answer 2

Answer 3

\(A=1+2+2^2+...+2^{2002}\)

\(2A=2+2^2+2^3+...+2^{2003}\)

\(2A-A=\left(2+2^2+2^3+...+2^{2003}\right)-\left(1+2+2^2+...+2^{2002}\right)\)

\(A=2^{2003}-1\)

⇒ \(A=B\)

Answer 4

A=1+2+22+...+22002A=1+2+22+...+22002

2A=2+22+23+...+220032A=2+22+23+...+22003

2A−A=(2+22+23+...+22003)−(1+2+22+...+22002)2A−A=(2+22+23+...+22003)−(1+2+22+...+22002)

A=22003−1A=22003−1

⇒