Question

A soma da PG infinita, (1, 1/2, 1/4,...), é?
A) 1/2.
B) 1/4.
C) 2.
D) 4.
E) 8.

Answer 1

Resposta:

C) 2

Explicação passo-a-passo:

Tem que aplicar na fórmula da soma dos termos

Answer 2

Soma infinita de uma PG :

$\displaystyle \text S_\infty = \frac{\text a_1}{1-\text q }$

Temos a PG :,

$\displaystyle (1,\frac{1}{2},\frac{1}{4},...)$

$\text a_1 = 1$

$\displaystyle \text q = \frac{\text a_2}{\text a_1} \to \text q = \frac{\frac{1}{2}}{1} \to \boxed{\text q = \frac{1}{2}}$

Substituindo na fórmula :

$\displaystyle \text S_\infty = \frac{\text a_1}{1-\text q }$

$\displaystyle \text S_\infty = \frac{1}{1-\frac{1}{2} }$

$\displaystyle \text S_\infty = \frac{1}{\frac{1}{2} }$

$\displaystyle \text S_\infty = 1.\frac{2}{1}$

$\huge\boxed{\displaystyle \text S_\infty = 2}$

Letra C