Select the FIRST correct reason why the given series converges.

A. Convergent geometric series
B. Convergent p series
C. Integral test
D. Comparison with a convergent p series
E. Converges by limit comparison test
F. Converges by alternating series test

1. $\displaystyle \sum_{n=2}^\infty \frac{7}{n (\ln (n))^2 }$
2. $\displaystyle \sum_{n=1}^\infty (-1)^n \frac{\sqrt{n}}{n +9}$
3. $\displaystyle \sum_{n=1}^\infty \frac{n^2+ \ln(n)}{n^2-8^n}$
4. $\displaystyle \sum_{n=1}^\infty \left( \frac{-e }{ \pi} \right)^n$
5. $\displaystyle \sum_{n=1}^\infty \frac{n^2+\sqrt{n}}{n^4-9}$
6. $\displaystyle \sum_{n=1}^\infty \frac{\sin^2 (4 n)}{n^2}$