Exercices corrigés
| Exercice 1. Calculer les sommes S,T,U suivantes : {\begin{array}{rl}S&=\dbinom n0+\dbinom n3+\dbinom n6+\cdots\\\\T&=\dbinom n1+\dbinom n4+\dbinom n7+\cdots\\\\U&=\dbinom n2+\dbinom n5+\dbinom n8+\cdots\end{array}} |
| Exercice 2. Calculer les sommes S,T,U,V suivantes : {\begin{cases}S=\dbinom n0+\dbinom n4+\dbinom n8+\cdots\\\\T=\dbinom n1+\dbinom n5+\dbinom n9+\cdots\\\\U=\dbinom n2+\dbinom n6+\dbinom n{10}+\cdots\\\\V=\dbinom n3+\dbinom n7+\dbinom n{11}+\cdots\end{cases}} |
| Exercice 3. Calculer la somme {\displaystyle\binom{n}{0}-3\displaystyle\binom{n}{2}+3^2\displaystyle\binom{n}{4}-3^3\displaystyle\binom{n}{6}+\cdots} |
| Exercice 4. Calculer {S_{n}=\displaystyle\sum_{k\ge0}(-1)^{k}\binom{n}{2k}} et {T_{n}=\displaystyle\sum_{k\ge0}(-1)^{k}\binom{n}{2k+1}}. |