Question

Determine a soma da PG (1/5, 1/20, 1/80...).

Answer 1

PG:

$\left( \dfrac{1}{5} ;\, \dfrac{1}{20};\, \dfrac{1}{80};...\right)$

Dados:

$a_1= \frac{1}{5} \\ \\ a_2= \frac{1}{20} \\ \\ q= \frac{1}{4}$

Soma dos termos da PG infinita:

$S_n= \dfrac{a_1}{1-q} \\ \\ \\ S_n= \dfrac{ \frac{1}{5} }{1- \frac{1}{4} } \\ \\ \\ S_n= \dfrac{ \frac{1}{5} }{ \frac{3}{4} } \\ \\ \\ \boxed{S_n= \frac{4}{15} }$