Which of the following statements is true for the series given below?

$$S_n=1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+\dots+\frac{1}{\sqrt{n}}$$

1. $S_n$ converges to $\log(\sqrt{n})$
2. $S_n$ converges to $\sqrt{n}$
3. $S_n$ converges to $\exp(\sqrt{n})$
4. $S_n$ diverges