Question

calcule o valor de x em que x + x/2 + x/4 +... = 30

Answer 1

$x + (x/2) + (x/4) + ... = 30$

$a_{1} = x$
$a_{2} = x/2$

$q = a_{2}/a_{1} = (x/2)/x=(x/2)*(1/x) => q = 1/2$

0 < q < 1 => Soma infinita

$S_{n} =a_{1}/(1-q)$
$30=x/(1-[1/2])$
$30=x/([2/2]-[1/2])$
$30=x/([2-1]/2)$
$30=x/(1/2)$
$30*(1/2)=x$
$x=30/2$
$x=15$