Question

Determine a soma dos termos da P.G. (1, 2, 4, ..., 1024).

Answer 1

Resposta:

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}}

Explicação passo-a-passo: