calculus - For what values of $k$ to both of the following series converge?

I'm taking the AP Calculus BC Exam next week and ran into this problem with no idea how to solve it. Unfortunately, the answer key didn't provide explanations, and I'd really, really appreciate it if someone could explain how to solve this problem, and why the answer is 4. It's a non-calculator question.

For which of the following values of k do both

$$\sum\limits_{n=1}^\infty\left(\frac3k\right)^n\;\;\;\text{ and}\;\;\;\;\; \sum\limits_{n=1}^\infty\frac{(3-k)^n}{\sqrt{n+3}}$$ converge?

Answer choices: None, 2, 3, 4, 5.