Question

Determine a soma dos termos das seguintes progressões geométricas infinitas (8,4,2...)

Answer 1

$\mathsf{a_1=8}\\\\\mathsf{r=\dfrac{2}{4}=\dfrac{1}{2}}\\\\\\\mathsf{Soma~de~uma~P.G:~S_n=\dfrac{a_1.(r^n-1)}{r-1}}\\\\\\\\\mathsf{\lim_{n \to \infty} \dfrac{8.(\frac{1}{2}^n-1)}{\frac{1}{2}-1}}\\\\\\\\\mathsf{\lim_{n \to \infty}\dfrac{8.(0-1)}{-\frac{1}{2}}}\\\\\\\mathsf{\lim_{n \to \infty} \dfrac{-8}{-\frac{1}{2}}}\\\\\\\mathsf{\lim_{n \to \infty} 8\cdot2=16}$

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