Answer
Diverges
Work Step by Step
We have: $\lim\limits_{k \to \infty} (\dfrac{k}{k+3})^{2k}=\lim\limits_{k \to \infty} (\dfrac{k+3}{k})^{-2k}\\=\lim\limits_{k \to \infty} [(1+\dfrac{3}{k})^{k}]^{-2}\\=(e^3)^{-2}\\=e^{-6} \ne 0$
This implies that the given series diverges.
