Question

Na sequência (8,-4,2,-1,1...) calcule o limite da soma
Pra hoje por favor

Answer 1

Resolução da questão, veja:

Vamos retirar da questão algumas informações necessárias, veja:

$\mathsf{S_{n}=~?}}\\\\\ \mathsf{A_{1} = 8}}\\\\\\\ \mathsf{q=\dfrac{A_{2}}{A_{1}}}}\\\\\ \mathsf{q=\dfrac{-4}{8}}~=>~\large\boxed{\boxed{\boxed{\mathsf{q=\dfrac{-1}{2}}}}}}}}}}}}}}}}$

Pronto, agora vamos aplicar estes dados na fórmula do limite da soma dos termos da PG, vejamos:

$\mathsf{\displaystyle\lim_{n~\to~+\infty}S_{n} = \dfrac{A_{1}}{1-q}}}}}}\\\\\\\\\\ \mathsf{\displaystyle\lim_{n~\to~+\infty}S_{n} = \dfrac{8}{1-\bigg(\dfrac{-1}{2}\bigg)}}}\\\\\\\\\\ \mathsf{\displaystyle\lim_{n~\to~+\infty}S_{n}=\dfrac{8}{\dfrac{2+1}{2}}}}}\\\\\\\\\\ \mathsf{\displaystyle\lim_{n~\to~+\infty}S_{n} = \dfrac{8}{\dfrac{3}{2}}}}\\\\\\\\\\ \mathsf{\displaystyle\lim_{n~\to~+\infty}S_{n} = 8~\cdot~\dfrac{2}{3}}}\\\\\\\\\ \large\boxed{\boxed{\boxed{\boxed{\boxed{\mathsf{\displaystyle\lim_{n~\to~+\infty}S_{n} = \dfrac{16}{3}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

Espero que te ajude. '-'