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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 \(w = \lim_{n\to\infty} w_n\).
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 \(w = \lim_{n\to\infty} w_n\).