grandes-ecoles 2021 Q11c

grandes-ecoles · France · x-ens-maths2__mp Sequences and Series Evaluation of a Finite or Infinite Sum

Deduce that, for all $x \in \mathbb{R}$, $$\sin(\pi x) = \pi x \lim_{n \rightarrow +\infty} \prod_{k=1}^{n}\left(1 - \frac{x^2}{k^2}\right).$$

Deduce that, for all $x \in \mathbb{R}$,
$$\sin(\pi x) = \pi x \lim_{n \rightarrow +\infty} \prod_{k=1}^{n}\left(1 - \frac{x^2}{k^2}\right).$$