For $n \in \mathbb{N}$, which of the following is true?

1. $\sqrt{n+1}-\sqrt{n}>\frac{1}{\sqrt{n}}$ for all, except possibly finitely many $n$

2. $\sqrt{n+1}-\sqrt{n}<\frac{1}{\sqrt{n}}$ for all, except possibly finitely many $n$

3. $\sqrt{n+1}-\sqrt{n}>1$ for all, except possibly finitely many $n$

4. $\sqrt{n+1}-\sqrt{n}>2$ for all, except possibly finitely many $n$