Question

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

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