Question

me ajudem pfvr!!!

determine o valor dos limites das seguintes somas:

a) 1+ 1/2 + 1/4 + 1/8+ ...

b) 2+ 1/2 + 1/8 + 1/32+ ...​

Answer 1

Explicação passo-a-passo:

a) $\sf q=\dfrac{\frac{1}{2}}{1}$

$\sf q=\dfrac{1}{2}$

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

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

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

$\sf S=\dfrac{1}{1}\cdot\dfrac{2}{1}$

$\sf S=2$

b) $\sf q=\dfrac{\frac{1}{2}}{2}$

$\sf q=\dfrac{1}{4}$

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

$\sf S=\dfrac{2}{1-\frac{1}{4}}$

$\sf S=\dfrac{2}{\frac{3}{4}}$

$\sf S=\dfrac{2}{1}\cdot\dfrac{4}{3}$

$\sf S=\dfrac{8}{3}$