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

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

- $S_n$ converges to $\log(\sqrt{n})$
- $S_n$ converges to $\sqrt{n}$
- $S_n$ converges to $\exp(\sqrt{n})$
- $S_n$ diverges