«
  
»
Calcule a soma da pg ( 1,2,4,8.1024)


RESOLVENDO

\( a_{1}=1\\a_{2}=2 \)
Calculando a razão da P. G:
\( q=\dfrac{a_{2}}{a_{1}}=\dfrac{2}{1}=2 \)
______________________
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:
\( S_{n}=\dfrac{a_{1}(q^{n}-1)}{q-1}\\S_{11}=\dfrac{a_{1}(q^{11}-1)}{q-1}\\S_{11}=\dfrac{1(2^{11}-1)}{2-1}\\S_{11}=2^{11}-1\\S_{11}=2048-1\\boxed{\boxed{S_{11}=2047}} \)



TAREFAS SIMILARES: