Show that when $n$ tends to $+\infty$, we have an equivalent of the form: $$\sum_{k=1}^{n} \frac{1}{\sqrt{k}} \underset{n \to +\infty}{\sim} \lambda \sqrt{n},$$ where the constant $\lambda$ is to be determined.
Show that when $n$ tends to $+\infty$, we have an equivalent of the form:
$$\sum_{k=1}^{n} \frac{1}{\sqrt{k}} \underset{n \to +\infty}{\sim} \lambda \sqrt{n},$$
where the constant $\lambda$ is to be determined.