Answer
Divergent
Work Step by Step
We have: $a_k=\dfrac{(-4)^k}{ k^2}$
Now, $\lim\limits_{k \to \infty} a_k=\lim\limits_{k \to \infty} |\dfrac{(-4)^k}{ k^2}|$
Use L-hospitals Rule : $\lim\limits_{k \to \infty} a_k=\lim\limits_{k \to \infty} |\dfrac{(-4)^k \ \ln (-4)^2}{2}|\\=\infty \ne 0 $
We conclude that the given series is divergent by the divergence test.
