Question

Cmr với mọi n thuộc N^* thì

A= 4ⁿ⁺³+4ⁿ⁺²-4ⁿ⁺¹-4ⁿ chia hết cho 300

Answer 1

Ta có: \(A=4^{n+3}+4^{n+2}-4^{n+1}-4^n\)

\(A=4^{n-1}.4^4+4^{n-1}.4^3-4^{n-1}.4^2-4^{n-1}.4\)

\(A=4^{n-1}\left(4^4+4^3-4^2-4\right)=4^{n-1}.300\).

Vậy .......... (dpcm)

Answer 2

\(A=4^{n+3}+4^{n+2}-4^{n+1}-4^n\)

\(=4^{n-1}.4^4+4^{n-1}.4^3-4^{n-1}.4^2-4^{n-1}.4\)

\(=4^{n-1}\left(4^4+4^3-4^2-4\right)\)

\(=4^{n-1}.300⋮300\)

\(\Rightarrow A⋮300\left(đpcm\right)\)

Vậy...