\begin{exercice}On considère le triangle de Pascal ci-dessous.
	
\vspace{-0.5\baselineskip}\begin{center}
{\renewcommand{\arraystretch}{1.1}
\begin{tabular}{|c|c|c|c|c|c|c|c|}	
	\hline
	\backslashbox{$n$}{$k$}&0&1&2&3&4&5&\ldots\\
	\hline
	0&1&\cellcolor{A3}&\cellcolor{A3}&\cellcolor{A3}&\cellcolor{A3}&\cellcolor{A3}&\cellcolor{A3}\\
	\hline
	1&1&1&\cellcolor{A3}&\cellcolor{A3}&\cellcolor{A3}&\cellcolor{A3}&\cellcolor{A3}\\
	\hline
	2&1&2&1&\cellcolor{A3}&\cellcolor{A3}&\cellcolor{A3}&\cellcolor{A3}\\	
		\hline
	3&1&3&3&1&\cellcolor{A3}&\cellcolor{A3}&\cellcolor{A3}\\
		\hline
	4&1&4&6&4&1&\cellcolor{A3}&\cellcolor{A3}\\
		\hline
	5&1& 5&10&10&5&1&\cellcolor{A3}\\
		\hline
	6&&&&&&&\\
	\hline
	\end{tabular}}
\end{center}
\begin{enumerate}
	\item 	\begin{enumerate}
		\item Lire $\covec 5 3 $ et $\covec 5 5$ dans le tableau.
		\item Déterminer $\covec 6 2$, $\covec 6 3$, $\covec 6 4$ et $\covec 6 5$.
	\end{enumerate}
	\item Démontrer que si $n$ et $k$ sont deux entiers tels que $k\leqslant n-2$, alors :
	
	$\covec{n+2}{k+2}=\covec{n}{k}+2\covec{n}{k+1}+\covec{n}{k+2}$.
\end{enumerate}


\end{exercice}
