Respostas

2013-06-26T19:49:00-03:00
  • Usuário do Brainly
2013-06-26T23:07:19-03:00

Observe que:

 

\text{S}_{\text{n}}=\dfrac{\text{a}_1\cdot(\text{q}^{\text{n}}-1)}{\text{q}-1}

 

Note que:

 

\text{q}=\dfrac{\text{a}_2}{\text{a}_1}=\dfrac{\frac{1}{2}}{\frac{1}{4}}=\dfrac{1}{2}\cdot\dfrac{4}{1}=2

 

Logo:

 

\text{S}_{11}=\dfrac{\frac{1}{4}\cdot(2^{11}-1)}{2-1}=\dfrac{\frac{1}{4}\cdot2~047}{1}=\dfrac{2~047}{4}

 

Portanto, a soma dos 11 primeiros termos da P.G. (1/4, 1/2, 1, 2, 4, ...) é \dfrac{2~047}{4}.

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