Match each of the following with the correct statement.
A. The series is absolutely convergent.
C. The series converges, but is not absolutely convergent.
D. The series diverges.

1. $\displaystyle \sum_{n=1}^\infty (-1)^{n+1}\frac{(3 + n) 4^n}{(n^2) 4^{2 n}}$
2. $\displaystyle \sum_{n=1}^\infty \frac{ (n + 4)!}{n! 3^n}$
3. $\displaystyle \sum_{n=1}^\infty \frac{(-1)^{n+1} }{3 n + 8}$
4. $\displaystyle \sum_{n=1}^\infty \frac{(-3)^{n}}{n^5}$
5. $\displaystyle \sum_{n=1}^\infty \frac{\sin (6 n)}{n^4}$