Question

Cho A = 1+2+2²+...+2²⁰⁰²

Cho B = 2²⁰⁰³ - 1

so sánh A và B

Answer 1

A = 1 + 2 + 2² + ....... + 2²⁰⁰²

2A = 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 - 1

Mà 2²⁰⁰³ - 1 = 2²⁰⁰³ - 1

Vậy A = B

Answer 2

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

2A=2+\(2^2\)+\(2^3\)+...+\(2^{2002}\)+\(2^{2003}\)

-

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

\(\Rightarrow2A-A=2^{2003}-1\)

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

Vì: \(2^{2003}-1=2^{2003}-1\)

\(\Rightarrow A=B\)

Vậy A=B