Question

Determine x na igualdade: x + 2x + 4x + ... + 256x = 2555​

Answer 1

Resposta:

Explicação passo a passo:

$PG$  

$(x;2x;4x........256x)$

$a_{1}=x$

$q=2$

$a_{n}=256x$

$S_{n}=2555$

$a_{n}=a_{1}\:.\:q^{(n-1)}$

$256x=x\:.\:2^{(n-1)}$

$2^{(n-1)}=256$

$2^{(n-1)}=2^{8}$

$n-1=8$

$n=8+1$

$n=9$

$S_{n}=\frac{a_{1}.(q^{n}-1) }{q-1}$

$2555=\frac{x.(2^{9}-1) }{2-1}$

$2555=\frac{x.(512-1) }{1}$

$2555=x\:.\:511$

$x=\frac{2555}{511}$

$x=5$