1. Decide if the following series are convergent or divergent. \[ \sum_{n=1}^\infty \frac{1}{n^2+9} \qquad \qquad \sum_{n=7}^\infty \frac{\ln(n)}{n} \qquad \qquad \sum_{n=1}^\infty \mathrm{e}^{-2n} \]
2. Why can’t the integral test be applied to decide the convergence/divergence of these series? \[ \sum_{n=1}^\infty \frac{\sec(\pi n)}{n^3} \qquad\quad \sum_{n=1}^\infty \frac{\cos(\pi n)}{\sqrt{n}} \qquad\quad \sum_{n=1}^\infty \frac{\cos^2(n)}{1+n^2} \]