Question

Calcule a soma das 10 parcelas da série em PG 1 + 1/2 + 1/4 + 1/8...

Answer 1

$sn = \frac{a1( {q}^{n} - 1) }{q - 1}$

$sn = \frac{1( { \frac{1}{2} }^{10} - 1 )}{ \frac{1}{2} - 1}$

$sn = \frac{ \frac{1}{1024} - 1}{ \frac{ - 1}{2} }$

$sn = \frac{ \frac{1}{1024} - \frac{1024}{1024} }{ \frac{ - 1}{2} }$

$sn = \frac{ \frac{ - 1023}{1024} }{ \frac{ - 1}{2} }$

$sn = \frac{ - 1023}{1024} \times \frac{ - 2}{1}$

$sn = \frac{2046}{1024}$

Ou, simplificando:

$sn = \frac{1023}{512}$