Question

calcule a soma da pg ( 1,2,4,8...1024) 

Answer 1

$a_{1}=1\\a_{2}=2$

Calculando a razão da P.G:

$q=\dfrac{a_{2}}{a_{1}}=\dfrac{2}{1}=2$
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Achando 'n':

$a_{n}=a_{1}\cdot q^{n-1}\\1024=1\cdot 2^{n-1}\\2^{10}=2^{n-1}\\10=n-1\\n=10+1\\n=11$

Agora, achando a soma dos 11 primeiros termos da P.G:

$S_{n}=\dfrac{a_{1}(q^{n}-1)}{q-1}\\\\\\S_{11}=\dfrac{a_{1}(q^{11}-1)}{q-1}\\\\\\S_{11}=\dfrac{1(2^{11}-1)}{2-1}\\\\\\S_{11}=2^{11}-1\\\\\\S_{11}=2048-1\\\\\\\boxed{\boxed{S_{11}=2047}}$