Question

o limite da soma infinita dos termos da p.g (1/4 + 1/20 + 1/100 ... + ...)

Answer 1

$S=\frac{1}{4}+\frac{1}{20}+\frac{1}{100}+\cdots$

Repare que a razão dessa PG é q = 1/5, então:

$\lim S=\frac{a_1}{1-q}\\\\\lim S=\frac{\frac{1}{4}}{1-\frac{1}{5}}\\\\\frac{\frac{1}{4}}{\frac{4}{5}}\\\\\frac{1}{4}\cdot\frac{5}{4}\\\\\boxed{\frac{5}{16}}$