Question

Calcular a soma dos termos da P.G, infinita ( 1,1/4 , 1/16,...)

Answer 1

$PG~\left( 1, \dfrac{1}{4} , \dfrac{1}{16}, ... \right)\\\\\\ a_1=1\\\\ q= \dfrac{1}{16}: \dfrac{1}{4}\to~~ \dfrac{1}{16}\times4\to~~ \dfrac{4}{16}\to~~ q=\dfrac{1}{4}\\\\\\\\ S_n= \dfrac{a_1}{1- q} \to~~ S_n= \dfrac{1}{1- \dfrac{1}{4} } \to~~ S_n= \dfrac{1}{ \dfrac{4-1}{4} } \to~~ S_n= \dfrac{1}{ \dfrac{3}{4} } \to\\\\ S_n=1\times \dfrac{4}{3} \to \large\boxed{S_n= \frac{4}{3} }$