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\begin{document}%%%%%%%%%%b{gedeonInfo}%%%%%%%%%
%%--Document N° 1483426181937--
%%--Utilisation de l\'expression conjuguée--
%%%%%%%%%%e{gedeonInfo}%%%%%%%%%


\begin{exercise}
$\vspace*{-0.35cm}$

\begin{enumerate}
\item Pour tout entier $n$, montrer que l'inverse de $\sqrt{n}+\sqrt{n+1}$ est
$\sqrt{n+1}-\sqrt{n}$.

\item En d\'{e}duire la valeur exacte de:%
\[
S=\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}%
}+\cdots+\frac{1}{\sqrt{360}+\sqrt{361}}.
\]

\end{enumerate}
\end{exercise}


\end{document}