grandes-ecoles 2024 Q10

grandes-ecoles · France · mines-ponts-maths2__psi Sequences and Series Asymptotic Equivalents and Growth Estimates for Sequences/Series
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.