grandes-ecoles 2024 Q11

grandes-ecoles · France · mines-ponts-maths2__psi Indefinite & Definite Integrals Definite Integral as a Limit of Riemann Sums

Deduce the limit: $$\lim_{n \rightarrow +\infty} \sum_{i=1}^{n-1} \frac{1}{\sqrt{i(n-i)}}.$$

Deduce the limit:
$$\lim_{n \rightarrow +\infty} \sum_{i=1}^{n-1} \frac{1}{\sqrt{i(n-i)}}.$$