Question

sendo n um numero natural, a expressao (2ⁿ⁺¹+2ⁿ⁺²) . (3ⁿ⁺²-3ⁿ⁺¹) , simplificada tem qual valor? _________________
6 ⁿ⁺²

Answer 1

Resposta:

Explicação passo-a-passo:

$(2^{n+1}+2^{n+2})(3^{n+2}-3^{n+1})=\\\\=2^{n+1}.3^{n+2}-2^{n+1}.3^{n+1}+2^{n+2}.3^{n+2}-2^{n+2}.3^{n+1}=\\\\=2^{n+1}.3^{n+1}.3-(2.3)^{n+1}+(2.3)^{n+2}-2.2^{n+1}.3^{n+1}=\\\\=3.(2.3)^{n+1}-6^{n+1}+6^{n+2}-2.(2.3)^{n+1}=\\\\=3.6^{n+1}-6^{n+1}+6^{n+2}-2.6^{n+1}=\\\\=2.6^{n+1}+6^{n+2}-2.6^{n+1}=\\\\=6^{n+2}$