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![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(A=4+4^2+4^3+...+4^{60}=4\left(1+4+4^2+...+4^{59}\right)⋮4\)
b) \(A=4+4^2+4^3+...+4^{60}=4\left(1+4\right)+4^3\left(1+4\right)+...+4^{59}\left(1+4\right)=4.5+4^3.5+...+4^{59}.5=5\left(4+4^3+...+4^{59}\right)⋮5\)
c) \(A=4+4^2+4^3+...+4^{60}=4\left(1+4+4^2\right)+4^4\left(1+4+4^2\right)+...+4^{58}\left(1+4+4^2\right)=4.21+4^4.21+...+4^{58}.21=21\left(4+4^4+...+4^{58}\right)⋮21\)
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
![](https://rs.olm.vn/images/avt/0.png?1311)
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 \(A⋮3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A=2.(1+2)+..........+2^59.(1+2)
A=2.3+.........+2^59.3
A=3.(2+....+2^59) chia hết cho 3
Vậy suy ra A chia hết cho 3
A=2.(1+2+2^2)+........+2^58.(1+2+2^2)
A=2.7+..........+2^58.7
A=7.(2+.....+2^58) chia hết cho 7
Vậy A chia hết cho 7
A=2.(1+2+2^2+2^3)+.........+2^57.(1+2+2^2+2^3)
A=2.15+...........+2^57.15
A=15.(2+2^57) chia hết cho 15
Vậy A chia hết cho 15
a) \(A=2+2^2+2^3+2^4+...+2^{60}\)
\(=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{59}+2^{60}\right)\)
\(=2\left(2+1\right)+2^3\left(2+1\right)+...+2^{59}\left(2+1\right)\)
\(=3\left(2+2^3+...+2^{59}\right)⋮3\)
Vậy \(A⋮3\)
b) \(A=2+2^2+2^3+2^4+...+2^{60}\)
\(=\left(2+2^3\right)+\left(2^2+2^4\right)+...+\left(2^{58}+2^{60}\right)\)
\(=2\left(1+2^2\right)+2^2\left(1+2^2\right)+...+2^{58}\left(1+2^2\right)\)
\(=5\left(2+2^2+...+2^{58}\right)⋮5\)
Vậy \(A⋮5\)
c) \(A=2+2^2+2^3+2^4+...+2^{60}\)
\(=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{58}+2^{59}+2^{60}\right)\)
\(=2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+..+2^{58}\left(1+2+2^2\right)\)
\(=7\left(2+2^4+...+2^{58}\right)⋮7\)
Vậy \(A⋮7\)