Question

Chứng minh rằng : \(3^{n+2}-2^{n+4}+3^n+2^n\)chia hết cho 30 với mọi n nguyên dương.

Answer 1

A=9.3^n+3^n+2^n-16.2^n

.=10.3^n-3.5.2^n=10.3^n-3.10.2^(n-1)=30[3^(n-1)-2^(n-1)]

Answer 2

haha đùa tí

Answer 3

3^n (3^2+1) - 2^n (2^4-1)= 3^n.10-2^n.15= 3^n-1.30-2^n-1.30=30(3^n-1-2^n-1) chia heets cho 30

Chúc bạn học tốt...

Answer 4

Ta có: 3ⁿ⁺²-2ⁿ⁺⁴+3ⁿ+2ⁿ

= (3ⁿ⁺²+3ⁿ)-(2ⁿ⁺⁴-2ⁿ)

= 3ⁿ(3²+1)-2ⁿ(2⁴-1)

= 3ⁿ.10-2ⁿ.15

= 3^n-1.3.10-2^n-1.2.15

= 3^n-1.30-2^n-1.30

=30(3^n-1-2^n-1)

Vì \(30⋮30\Rightarrow30\left(3^{n-1}-2^{n-1}\right)⋮30\)

\(\Rightarrow3^{n+2}-2^{n+4}+3^n+2^n⋮30\)

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