Question

Calcule a soma dos termos da PG infinita (8,4,2,1,1/2)

Answer 1

Soma dos termos infinitos de uma P.G:

$S_{n}=\dfrac{a_{1}}{1-q}$

Essa fórmula só serve para progressões geométricas com razão entre 0 e 1
___________________

$a_{1}=8\\a_{2}=4\\\\q=a_{2}/a_{1}=4/8=1/2$

$S_{n}=\dfrac{a_{1}}{1-q}\\\\\\S_{n}=\dfrac{8}{1-\frac{1}{2}}\\\\\\S_{n}=\dfrac{8}{(\frac{1}{2})}\\\\\\S_{n}=8*\dfrac{2}{1}\\\\\\\boxed{\boxed{S_{n}=16}}$