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 $n$