Question

Cho \(A=2+2^2+2^3+2^4+...+2^{60}\)

Chứng tỏ 

a, A chia hết cho 3

b, A chia hết cho 5

c, A chia hết cho 7

 

Answer 1

a) \(A=2+2^2+2^3+2^4+...+2^{60}\)

\(=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{59}+2^{60}\right)\)

\(=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{59}\left(1+2\right)\)

\(=3\left(2+2^3+...+2^{59}\right)⋮3\)

Vậy \(A⋮3\)