Question

A=2 + 2^2 + 2^3 + ... + 2^10

Hỏi A có chia hết cho 3 ko ?

Answer 1

A = 2 + 2² + 2³ + ... + 2¹⁰

= (2 + 2²) + (2³ + 2⁴) + ... + (2⁹ + 2¹⁰)

= 2(1 + 2) + 2³(1 + 2) + ... + 2⁹(1 + 2)

= 3(2 + 2³ + ... + 2⁹) \(⋮\) 3

Vậy, A \(⋮\) 3

Answer 2

\(A=2+2^2+2^3+.....+2^{10}\)

\(\Leftrightarrow A=\left(2+2^2\right)+\left(2^3+2^4\right)+.....+\left(2^9+2^{10}\right)\)

\(\Leftrightarrow A=2\left(1+2\right)+2^3\left(1+2\right)+.....+2^9\left(1+2\right)\)

\(\Leftrightarrow A=2.3+2^3.3+.....+2^9.3\)

\(\Leftrightarrow A=3\left(2+2^3+.....+2^9\right)⋮3\)

Vậy \(A⋮3\)

Answer 3

Ta có: 2 + 2² + 2³ + ... + 2¹⁰
= (2 + 2²) + (2³ + 2⁴) + ... + (2⁹ + 2¹⁰)
= 2(1+2) + 2³(1+2) + ... + 2⁹(1+2)
= 2.3 + 2³.3 + ... + 2⁹.3
= 3(2 + 2³ + ... + 2⁹)
Vì 3(2 + 2³ + ... + 2⁹) ⋮ 3
Nên (2 + 2² + 2³ + ... + 2¹⁰) ⋮ 3
Vậy A ⋮ 3