Question

Qual é o limite da soma :
$\frac{5}{7 } + \frac{1}{7} + \frac{1}{35} + \frac{1}{175} + \frac{1}{875} + ...$
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Answer 1

Resposta:

Explicação passo-a-passo:

Cálculo da razão

$q=\dfrac{\frac{1}{7}}{\frac{5}{7}}=\dfrac{1}{7}.\dfrac{7}{5}=\dfrac{1}{5}\\\\\\S=\dfrac{a_1}{1-q}\\\\\\S=\dfrac{\frac{5}{7}}{1-\frac{1}{5}}\\\\\\S=\dfrac{\frac{5}{7}}{\frac{5}{5}-\frac{1}{5}}\\\\\\S=\dfrac{\frac{5}{7}}{\frac{4}{5}}\\\\\\S=\frac{5}{7}.\frac{5}{4}\\\\\\\boxed{S=\frac{25}{28}}$