exo7 4025

On pose $u_{n,p} = \left({\frac1n \sum_{k=0}^{n-1} \Bigl(1+\frac kn\Bigr)^{1/p}}\right)^p$. Trouver : $v_p = \lim_{n\to\infty} u_{n,p}$, $v = \lim_{p\to\infty} v_p$, $w_n = \lim_{p\to\infty} u_{n,p}$ et $w = \lim_{n\to\infty} w_n$.