Question

Dada a pg com a1 = 5 e q=2/5, calcule a soma dos infinitos termos desta pg

Answer 1

$S_{\infty} = \frac{a1}{1 - q} \\ S_{\infty} = \frac{5}{1 -(2/5)} \\ S_{\infty} = \frac{5}{3/5} \\ S_{\infty} = \frac{25}{3}$

25/3 = 8,33

Answer 2

Explicação passo-a-passo:

$\sf S=\dfrac{a_1}{1-q}$

$\sf S=\dfrac{5}{1-\frac{2}{5}}$

$\sf S=\dfrac{5}{\frac{5-2}{5}}$

$\sf S=\dfrac{5}{\frac{3}{5}}$

$\sf S=\dfrac{5}{1}\cdot\dfrac{5}{3}$

$\sf \red{S=\dfrac{25}{3}}$