Question

Cho A= 4 + 2^2 + 2^3 + 2^4 +...+ 2^20. Hỏi A có chia hết cho 128 không?

Answer 1

2A - A= 2²¹chia hết cho 2⁷

suy ra A chia hết cho 128

Answer 2

2A-A=2²¹ chia het cho2⁷,suy ra Achia het cho 128

Answer 3

2A-A=2\(^{21}\)chia hết cho2\(^7\)

=>A chia hết cho 128

Answer 4

A chia hết cho 128

Answer 5

\(A=4+2^2+2^3+2^4+...+2^{20}\)

=> \(A=2^2+2^2+2^3+2^4+...+2^{20}\)

=>\(2A=2\left(2^2+2^2+2^3+2^4+...+2^{20}\right)\)

=> \(2A=2^3+2^3+2^4+2^5+...+2^{21}\)

=> \(2A-A=2^3+2^{21}-\left(2^2+2^2\right)\)

=>\(A=8+2^{21}-8\)

=> \(A=2^{21}\)

mà \(2^{21}⋮2^7\)

=>\(2^{21}⋮128\)

=> \(A⋮128\)