Question

cho A = 1+2+2^2+2^3+...+2^2003 . So sánh A với B = 2^2004-1

Answer 1

A = 1 + 2 + 2² + 2³ + ... + 2²⁰⁰³

2A = 2 + 2² + 2³ + 2⁴ + ... + 2²⁰⁰⁴

2A - A = (2 + 2² + 2³ + 2⁴ + ... + 2²⁰⁰⁴) - (1 + 2 + 2² + 2³ + ... + 2²⁰⁰³)

A = 2²⁰⁰⁴ - 1 = B

Answer 2

Ta có: \(A=1+2+2^2+2^3+...+2^{2003}\)

\(\Rightarrow2A=2+2^2+2^3+2^4+...+2^{2004}\)

\(\Rightarrow2A-A=\left(2+2^2+2^3+2^4+...+2^{2004}\right)-\left(1+2+2^2+2^3+...+2^{2003}\right)\)

\(\Rightarrow A=2^{2004}-1\)

Mà \(B=2^{2004}-1\)

\(\Rightarrow B=A\) hay A = B

Vậy A = B