4 Sean $p$ , $q$ dos enteros, $q\geq p\geq 0$ . Sea $n \geq 2$ un entero y sean $a_0=0, a_1 \geq 0, a_2, \ldots, a_{n-1},a_n = 1$ números reales tales que \[ a_{k} \leq \frac{ a_{k-1} + a_{k+1} } 2 , \ \forall \ k=1,2,\ldots, n-1 . \] Demuestre que \[ (p+1) \sum_{k=1}^{n-1} a_k^p \geq (q+1) \sum_{k=1}^{n-1} a_k^q . \] Valentin