Question

Calcule o limite da soma dos ifinitos da pg (2/3+2/3+2/27....+..)

Answer 1

$a_{1= \frac{2}{3} } \\ \\ a_{2}= \frac{2}{9} \\ \\ a_{3} = \frac{2}{27}$

Cálculo da razão da p.g.

$q= \frac{ a_{2} }{ a_{1} } \\ \\ q= \frac{ \frac{2}{9} }{ \frac{2}{3} } \\ \\ q= \frac{2}{9}. \frac{3}{2} \\ \\ q= \frac{1}{3} }$

Cálculo da soma dos infinitos termos da p.g.

$S= \frac{ a_{1} }{1-q} \\ \\ S= \frac{ \frac{2}{3} }{1- \frac{1}{3} } \\ \\ S= \frac{ \frac{2}{3} }{ \frac{3-1}{3} } \\ \\ S= \frac{ \frac{2}{3} }{ \frac{2}{3} } \\ \\ S=1$