Question

3ⁿ⁺³+2ⁿ⁺³-3ⁿ⁺²+2ⁿ⁺² chia hết cho 6

Answer 1

ta có:\(3^{n+3}+2^{n+3}-3^{n+2}+2^{n+2}\)

=\(3^n\cdot3^3+2^n\cdot2^3-3^n\cdot3^2+2^n\cdot2^2\)

=\(3^n\cdot\left(3^3-3^2\right)+2^n\cdot\left(2^3+2^2\right)\)

=\(3^n\cdot18+2^n\cdot12\)

=\(3^n\cdot3\cdot6+2^n\cdot2\cdot6\)

=\(\left(3^n\cdot3+2^n\cdot2\right)\cdot6\)

=>\(\left(3^n\cdot3+2^n\cdot2\right)\cdot6\)chia hết cho 6

=>\(3^{n+3}+2^{n+3}-3^{n+2}+2^{n+6}\)chia hết cho 6

=>ĐPCM