Question

Cho A=2+\(2^2\)+\(2^3\)+.......\(2^{60}\).Chung to rang:A chia het cho 3,A chia het cho 5,A chia het cho 7

Answer 1

Ta có : A = 2 + 2² + 2³ + 2⁴ + .. + 2⁵⁹ + 2⁶⁰

= (2 + 2²) + (2³ + 2⁴) + .. + (2⁵⁹ + 2⁶⁰)

= 2(2 + 1) + 2³(2 + 1) + ... + 2⁵⁹(2 + 1) 

= (2 + 1)(2 + 2³ + ... + 2⁵⁹) = 3(2 + 2³ + ... + 2⁵⁹) \(⋮\)3

Answer 2

giup minh voi

Answer 3

A = 2 + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + ... + 2⁵⁸ + 2⁵⁹ + 2⁶⁰

= (2 + 2² + 2³) + (2⁴ + 2⁵ + 2⁶) + ... + (2⁵⁸ + 2⁵⁹ + 2⁶⁰)

= 2(1 + 2 + 2²) + 2⁴(1 + 2 + 2²) + ... + 2⁵⁸(1 + 2 + 2²) 

= (1 + 2 + 2²)(2 + 2⁴ + ... + 2⁵⁸) 

= 7(2 + 2⁴ + ... + 2⁵⁸) \(⋮\)7

Answer 4

A = 2 + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷ + 2⁸ + ... + 2⁵⁷ + 2⁵⁸ + 2⁵⁹ + 2⁶⁰

= (2 + 2² + 2³ + 2⁴) + (2⁵ + 2⁶ + 2⁷ + 2⁸) + ... + (2⁵⁷ + 2⁵⁸ + 2⁵⁹ + 2⁶⁰)

= 2(1 + 2 + 2² + 2³) + 2⁵(1 + 2 + 2² + 2³) + ... + 2⁵⁷(1 + 2 + 2² + 2³)

= (1 + 2 + 2² + 2³)(2 + 2⁵ + ... + 2⁵⁷)

= 15(2 + 2⁵ + ... + 2⁵⁷) = 3.5(2 + 2⁵ + ... + 2⁵⁷)\(⋮\)5