Answer
Diverges
Work Step by Step
Apply the n-th term test. For $a_k \to 0$, the series diverges.
Therefore, $ L=\lim\limits_{k \to \infty} \dfrac{1}{4+2^{-k}} \\=\dfrac{1}{4+0}\\=\dfrac{1}{4} \ne 0$
So, we can conclude that the given series diverges by the n-th term test.