For each of the following, determine if the series converges. Be sure that you can rigorously demonstrate your answer!

? converges diverges  1. $\displaystyle \sum\limits_{n=5}^{\infty} {n^{2}\over n^{6} + 4 n^{3} + 4}$

? converges diverges  2. $\displaystyle \sum\limits_{n=1}^{\infty} {2\over (5 n - 1)^{3}}$

? converges diverges  3. $\displaystyle \sum\limits_{n=1}^{\infty} {5 n\over (5 n + 1)}$

? converges diverges  4. $\displaystyle \sum\limits_{n=5}^{\infty} {n + 5\over n^2 + 10 n + 2}$

? converges diverges  5. $\displaystyle \sum\limits_{n=0}^{\infty} {2\over n^2 + 5}$

? converges diverges  6. $\displaystyle \sum\limits_{n=1}^{\infty} \frac{1}{\ln(5^{n})}$

? converges diverges  7. $\displaystyle \sum\limits_{n=1}^{\infty} {n + 5^n\over n 5^n}$