Question

Chứng minh rằng

M= 3ⁿ⁺³+3ⁿ⁺¹+2ⁿ⁺³+2ⁿ⁺²

Chia hết cho 6

Answer 1

Trả lời:

Ta có:M= \(3^{N+3}+3^{N+1}+2^{N+3}+2^{N+2}\)

= \(3^N.3^3+3^N.3^1+2^N.2^3+2^N.2^2\)

=\(3^N.27+3^N.3+2^N.8+2^N.4\)

=\(3^N.\left(27+3\right)+2^N.\left(8+4\right)\)

Hay :\(3^N.30+2^N.12\)

Vì:\(30⋮6\) và\(12⋮6\)

Nên : \(3^n.30+2^n.12⋮6\)

Vậy: \(3^{N+3}+3^{N+1}+2^{N+3}+2^{N+2}\)\(⋮\)