Question

resolva a equacao em que o primeiro membro representa a soma de uma pg infini'a x+x/3+x/9+....=12

Answer 1

$x+ \dfrac{x}{3} + \dfrac{x}{9} +...=12$

$a_{1} =x$

$q= \dfrac{x}{3} :x=\dfrac{x}{3}.\dfrac{1}{x}=\dfrac{1}{3}$

$S_{n} =\dfrac{ a_{1} }{1-q}=\dfrac{ x }{1- \dfrac{1}{3} }=\dfrac{ x }{ \dfrac{3-1}{3} }=\dfrac{ x }{ \dfrac{2}{3} }=x.\dfrac{ 3 }{2}=\dfrac{ 3x }{2}$

$\dfrac{ 3x }{2}=12$

$3x=24$

$x= \dfrac{24}{3}$

$x=8$

$S=\{8\}$