C$.|r|1$

D$.|r|>1$

$3.$ Evaluate the following geometric sum.

$\frac{\frac{1}{2}\frac{1}{8}\frac{1}{32}\frac{1}{128}\text{c}\text{d}\text{o}\text{t}\text{s}\frac{1}{8192}}{\frac{1}{2}\frac{1}{8}\frac{1}{32}\frac{1}{128}\text{c}\text{d}\text{o}\text{t}\text{s}\frac{1}{8192}}=$

$($Simplify your answer. Type an integer or a fraction.$)$

$4.$ Evaluate the geometric series or state that it diverges.