Respostas

  • Usuário do Brainly
2013-06-03T15:15:57-03:00

Temos que:

 

\text{x}=\dfrac{2^{\text{n}+1}+2^{\text{n}}\cdot3^{\text{n}+1}-3^{\text{n}}}{6}

 

Observe que:

 

2^{\text{n}+1}=2^{\text{n}}\cdot2 e 3^{\text{n}+1}=3^{\text{n}}\cdot3

 

Desta maneira, segue que:

 

\text{x}=\dfrac{2^{\text{n}}\cdot2+2^{\text{n}}\cdot3^{\text{n}}\cdot3-3^{\text{n}}}{6}

 

Logo:

 

\text{x}=\dfrac{2^{\text{n}}\cdot2}{6}+\dfrac{2^{\text{n}}\cdot3^{\text{n}}\cdot3}{6}+\dfrac{3^{\text{n}}}{6}

 

 

\text{x}=\dfrac{2^{\text{n}}}{3}+2^{\text{n}-1}\cdot3^{\text{n}}-\dfrac{3^{\text{n}-1}}{2}