Question

Determine a soma da P.G infinita (1/3+2/9+2/27+...)


Ajuda ai galera!!!!!! Tenho até 11h para responder essa questão porfavor!

Answer 1

Essa sequencia é uma PAG.
S = (1/3) + (2/9) + (3/27) + (4/81) + ... I
multiplicando a soma pela razão da pg ( q = 1/3), obtemos:
S.1/3 = (1/9) + (2/27) + (3/81) + ... II

Subtraindo II de I
S - S/3 = 1/3 + (2/9 -1/9) + (3/27 - 2/27) + (4/81 - 3/81) + ...
2S/3 = 1/3 + 1/9 + 1/27 + 1/81 + ...
PG infinita de razão 1/3
Si = a1/ 1-q
Si = (1/3) /(1 - 1/3 )
Si = 1/2

2S/3 = 1/2
S = 3/4

Answer 2

Bom dia João!

Solução!

Formula da P.G infinita!

$S= \dfrac{a1}{1-q}$

$a1= \dfrac{1}{3} \\\\\\\ q= \dfrac{a2}{a1}\\\\\\\ q= \dfrac{2}{ \dfrac{9}{\dfrac{1}{3} } }\\\\\\\ q= \dfrac{2}{9} \times \dfrac{3}{1} \\\\\\ q= \dfrac{6}{9} \\\\\\\ q= \dfrac{2}{3}$


$S= \dfrac{1}{ \frac{3}{1- \dfrac{2}{3} } }\\\\\\\ S= \dfrac{1}{ \dfrac{3}{ \dfrac{3-2}{3} } }\\\\\\\ S= \dfrac{1}{ \frac{3}{ \dfrac{1}{3} } }\\\\\\\ S= \dfrac{1}{3}\times \dfrac{3}{1}\\\\\\\ S= \dfrac{3}{3} \\\\\\\ S=1$

Bom dia!
Bons estudos!