The Limit Comparison Test

Use any of the techniques we have discussed in class to determine the convergence/divergence of the following series.

1. $\displaystyle{\sum_{n=1}^\infty \frac{1}{\sqrt{n}}}$
2. $\displaystyle{\sum_{n=1}^\infty \frac{1}{5n}}$
3. $\displaystyle{\sum_{n=1}^\infty \frac{n}{2n-\sqrt{n}}}$