Question

[Hoàng Minh Thư]

Bài 1 : Cho A=2+2^2+2^3+....+2^2016.

Chứng minh A chia hết cho 7

Answer 1

[Dương Lam Hàng]

Ta có: \(A=2+2^2+2^3+2^4+....+2^{2016}\)

\(\Rightarrow A=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{2014}+2^{2015}+2^{2016}\right)\)

\(\Rightarrow A=2.\left(2+2+2^2\right)+2^4.\left(1+2+2^2\right)+...+2^{2014}.\left(1+2+2^2\right)\)

\(\Rightarrow A=2.7+2^4.7+....+2^{2014}.7\) 

\(\Rightarrow A=7.\left(2+2^4+....+2^{2014}\right)\) CHIA HẾT CHO 7

Vậy A chia hết cho 7

Answer 2

[Noo Phuoc Thinh]

A= 2+2²+2³+.........+2²⁰¹⁶

2A=2²+2³+.........+2²⁰¹⁷

 A=2+2²+2³+.............+3²⁰¹⁶

A= 2²⁰¹⁷-2