• Matéria: Matemática
  • Autor: hhgmo
  • Perguntado 9 anos atrás

Determine a soma de cada PG infinita

Anexos:

Respostas

respondido por: korvo
20
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}}}}.\\.

>>>>>>>>>>>>>>>>>>>>>>>

\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}}}}.\\.

>>>>>>>>>>>>>>>>>>>>>>>

\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

hhgmo: obg mano
korvo: espero que tenha entendido, d nd
hhgmo: s mano, agr entendi
korvo: blz então y
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