Answer
The series diverges as shown using the $Divergence$ $Test$
Work Step by Step
We can use the divergence test to evaluate this series by seeing if $\lim\limits_{n \to \infty} a_{n} \ne 0$, in which it would mean that the series diverges
$\lim\limits_{n \to \infty} a_{n} = \lim\limits_{n \to \infty} \frac{1}{4+e^-n} = \lim\limits_{n \to \infty} \frac{1}{4+e^-\infty} = \frac{1}{4 + 0} = \frac{1}{4} $
Since $ \frac{1}{4} \ne 0 $, by the divergence test, the series diverges.
