Question

$2^{n+3}$ ·$7^{n$+$7^{n +1$·$2^{n$-3·$14^{n$ se divide cu 6,oricare ar fi nr natural nenul n

Answer 1

2^(n+3) × 7^n  + 7^(n+1) × 2^n - 3×14^n=
=2^(n+3) × 7^n +7^(n+1) ×2^n - 3 × 2^n ×7^n=
=2^n × 7^n ×(2^3 ×7^0 +7^1 ×2^0 - 3 × 2^0 ×7^0) =
=2^n × 7^n ×(8×1 +7×1 - 3 × 1 ×1) =
=2^n × 7^n ×(8 +7 - 3) =
=2^n × 7^n  × 12 =
=2^n × 7^n  × 2×6 =
=2^(n+1) × 7^n  ×6  deci divizibil cu 6