Question

Determine a soma de cada PG infinita

Answer 1

E aí vei,

identifique os termos de cada P.G., e substitua-os na fórmula da soma da P.G. infinita:

$\begin{cases}S_\infty=?\\ q= \dfrac{a_2}{a_1}= \dfrac{1}{6}\div \dfrac{1}{2}= \dfrac{1}{3}\\\\ a_1= \dfrac{1}{2}\end{cases}$

$S_\infty= \dfrac{a_1}{1-q}~\to~S_\infty= \dfrac{ \dfrac{1}{2} }{1- \dfrac{1}{3} }~\to~S_\infty= \dfrac{1}{2}\div \dfrac{2}{3}~\to~\Large\boxed{\boxed{\boxed{S_\infty= \dfrac{3}{4}}}}.\\.$

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$\begin{cases}S_\infty=?\\ q= \dfrac{a_2}{a_1}= \dfrac{1}{10}\div1= \dfrac{1}{10}\\\\ a_1=1 \end{cases}$

$S_\infty= \dfrac{1}{1- \dfrac{1}{10} }~\to~S_\infty=1\div \dfrac{9}{10}~\to~\Large\boxed{\boxed{\boxed{S_\infty= \dfrac{10}{9}}}}.\\.$

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$\begin{cases}S_\infty=?\\ q= \dfrac{a_2}{a_1}= \dfrac{50}{100}= \dfrac{1}{2}\\\\ a_1=100 \end{cases}$

$S_\infty= \dfrac{100}{1- \dfrac{1}{2} }~\to~S_\infty=100\div \dfrac{1}{2}~\to~\Large\boxed{\boxed{\boxed{S_\infty=200}}}.\\.$

Ótimos estudos mano ;D