• Matéria: Matemática
  • Autor: Anônimo
  • Perguntado 3 anos atrás

Calcular o produto dos oito primeiros termos da P.G. \bigg( \dfrac{1}{8},\dfrac{1}{4},\dfrac{1}{2},...\bigg).

Respostas

respondido por: Math739
1

\large\displaystyle\text{$\begin{gathered}\sf{Leitura\,do\,problema:\begin{cases}\sf P.G.\bigg(\dfrac{1}{8},\dfrac{1}{4},\dfrac{1}{2},...\bigg)\\\sf P_8=?\end{cases}}\end{gathered}$}

\large\displaystyle\text{$\begin{gathered} \sf{C\acute{a}lculo\,de\, a_8  \, sendo\,a_1=\dfrac{1}{8},\,q=\dfrac{1}{4}:\dfrac{1}{8}=2\,e\,n=8  } \end{gathered}$}

\large\displaystyle\text{$\begin{gathered} \sf{   a_8=\dfrac{1}{8}\cdot2^7=\dfrac{128}{8}\Rightarrow a_8=16 } \end{gathered}$}

\large\displaystyle\text{$\begin{gathered} \sf{  Logo,o\, produto\,P_8\,\acute{e}:  } \end{gathered}$}

\large\displaystyle\text{$\begin{gathered} \sf{ |P_8|=\sqrt{\bigg(\dfrac{1}{8}\cdot16\bigg)^8}\Rightarrow |P_8|=\sqrt{2^8}\Rightarrow|P_8|=2^4,\, ent\tilde{a}o\,P_8=16   } \end{gathered}$}

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