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. $\displaystyle \sum_{n=1}^\infty \frac{(n+1)(6^2 -1)^n}{6^{2n}}$
2. $\displaystyle \sum_{n=1}^\infty \frac{(-1)^n}{3 n + 6}$
3. $\displaystyle \sum_{n=1}^\infty \frac{\sin(7 n)}{n^2}$
4. $\displaystyle \sum_{n=1}^\infty \frac{(-3)^n }{n^5}$
5. $\displaystyle \sum_{n=1}^\infty (-1)^n \frac{\sqrt{n}}{n +3}$