Which of the following series converge, use ratio or comparison test to demonstrate:
$\sum_{n=1}^{\infty} \dfrac{n}{n^2+\cos^2(n)}$
$\sum_{n=1}^{\infty} \dfrac{(-10)^n}{4^{2n+1}(n+1)}$
$\sum_{n=1}^{\infty} \dfrac{n!}{3^n}$
$\sum_{n=1}^{\infty} \dfrac{n}{(n+3)^3}$
Help much appreciated! Thanks!