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. \(\displaystyle{\sum_{n=1}^\infty \frac{n}{2n-\sqrt{n}}}\)