Exercices corrigés
| Exercice 1. Calculer le déterminant {D(m,p)=\begin{vmatrix}\binom m0&\binom m1&\ldots&\binom mp\phantom{\bigg|}\!\\\binom {m+1}0&\binom {m+1}1&\ldots&\binom {m+1}p\phantom{\bigg|}\!\\\vdots&\vdots&\vdots&\vdots\\\binom {m+p}0&\binom {m+p}1&\ldots&\binom {m+p}p\phantom{\bigg|}\!\end{vmatrix}} |
| Exercice 2. Calculer {D=\begin{vmatrix}\binom{n+1}1&1&0&\ldots&0\phantom{\bigg|}\!\\\binom{n+2}2&\binom{n+2}1&1&\ddots&\vdots\phantom{\bigg|}\!\\\vdots&\ddots&\ddots&\ddots&0\\\vdots&\ldots&\ldots&\binom{n+p-1}1&1\phantom{\bigg|}\!\\\binom{n+p}p&\binom{n+p}{p-1}&\ldots&\binom{n+p}2&\binom{n+p}1\phantom{\bigg|}\!\end{vmatrix}} |
| Exercice 3. Calculer le déterminant {D_p=\begin{vmatrix}\binom{1}1&1&0&\ldots&0\\\binom{2}2&\binom{2}1&1&\ddots&\vdots\phantom{\bigg|}\!\\\vdots&\ddots&\ddots&\ddots&0\\\vdots&\ldots&\ldots&\binom{p-1}1&1\phantom{\bigg|}\!\\\binom{p}p&\binom{p}{p-1}&\ldots&\binom{p}2&\binom{p}1\phantom{\bigg|}\!\end{vmatrix}} |