\begin{exercice}Pour chacune des suites représentées ci-dessous, dire quelle semble être sa limite quand $n$ tend vers $+\infty$.

\begin{enumerate}
  \item ~~

  \vspace{-\baselineskip}\begin{tikzpicture}[general,xscale=.6,yscale=0.6]
  \draw[quadrillageNIV2, xstep=1, ystep=1](0,0) grid(10,5);

\axeX{0}{10}{0,1,2,3,4,5,6,7,8,9,10};
\axeY{0}{5}{0,1,2,3,4,5};

%u_n=3+(-1)^n/(n+1)

\draw [color=C1]  (0,2) node {$\bullet$};
\draw [color=C1]  (1,3.5) node {$\bullet$};
\draw [color=C1]  (2,2.667) node {$\bullet$};
\draw [color=C1] (3,3.25) node {$\bullet$};
\draw [color=C1] (4,2.8) node {$\bullet$};
\draw [color=C1] (5,3.167) node {$\bullet$};
\draw [color=C1] (6,2.857) node {$\bullet$};
\draw [color=C1] (7,3.125) node {$\bullet$};
\draw [color=C1] (8,2.889) node {$\bullet$};
\draw [color=C1] (9,3.1) node {$\bullet$};
\draw [color=C1] (10,2.909) node {$\bullet$};
    \end{tikzpicture}
  \item ~~

  \vspace{-\baselineskip}\begin{tikzpicture}[general,xscale=.6,yscale=0.6]
  \draw[quadrillageNIV2, xstep=1, ystep=1](0,-5) grid(10,1);

\axeX{0}{10}{0,1,2,3,4,5,6,7,8,9,10};
\axeY{-5}{1}{-5,-4,-3,-2,-1,0,1};

%u_n=-2-3*(-0.6)^n
\draw [color=C1]  (0,-5) node {$\bullet$};
\draw [color=C1]  (1,-3.8) node {$\bullet$};
\draw [color=C1]  (2,-3.08) node {$\bullet$};
\draw [color=C1]  (3,-2.648) node {$\bullet$};
\draw [color=C1] (4,-2.389) node {$\bullet$};
\draw [color=C1] (5,-2.233) node {$\bullet$};
\draw [color=C1] (6,-2.14) node {$\bullet$};
\draw [color=C1] (7,-2.084) node {$\bullet$};
\draw [color=C1] (8,-2.05) node {$\bullet$};
\draw [color=C1] (9,-2.03) node {$\bullet$};
\draw [color=C1] (10,-2.018) node {$\bullet$};
    \end{tikzpicture}
  \item ~~

  \vspace{-\baselineskip}\begin{tikzpicture}[general,xscale=.6,yscale=0.06]
  \draw[quadrillageNIV2, xstep=1, ystep=10](0,0) grid(10,100);

\axeX{0}{10}{0,1,2,3,4,5,6,7,8,9,10};
\axeY{0}{100}{0,10,20,30,40,50,60,70,80,90,100};

%u_n=n^2
\draw [color=C1]  (0,0) node {$\bullet$};
\draw [color=C1]  (1,1) node {$\bullet$};
\draw [color=C1]  (2,2) node {$\bullet$};
\draw [color=C1]  (3,9) node {$\bullet$};
\draw [color=C1] (4,16) node {$\bullet$};
\draw [color=C1] (5,25) node {$\bullet$};
\draw [color=C1] (6,36) node {$\bullet$};
\draw [color=C1] (7,49) node {$\bullet$};
\draw [color=C1] (8,64) node {$\bullet$};
\draw [color=C1] (9,81) node {$\bullet$};
\draw [color=C1] (10,100) node {$\bullet$};
    \end{tikzpicture}
  \item ~~

  \vspace{-\baselineskip}\begin{tikzpicture}[general,xscale=.5,yscale=0.08]
  \draw[quadrillageNIV2, xstep=1, ystep=10](0,-50) grid(12,10);

\axeX{0}{12}{1,2,3,4,5,6,7,8,9,10,11,12};
\axeY{-50}{10}{-50,-40,-30,-20,-10,0,10};

%u_n=-n^{1.5}+6sin(n)
\draw [color=C1]  (0,0) node {$\bullet$};
\draw [color=C1]  (1,4.049) node {$\bullet$};
\draw [color=C1]  (2,2.627) node {$\bullet$};
\draw [color=C1]  (3,-4.349) node {$\bullet$};
\draw [color=C1] (4,-12.54) node {$\bullet$};
\draw [color=C1] (5,-16.933) node {$\bullet$};
\draw [color=C1] (6,-16.37) node {$\bullet$};
\draw [color=C1] (7,-14.58) node {$\bullet$};
\draw [color=C1] (8,-16.69) node {$\bullet$};
\draw [color=C1] (9,-24.53) node {$\bullet$};
\draw [color=C1] (10,-34.89) node {$\bullet$};
\draw [color=C1] (11,-42.48) node {$\bullet$};
\draw [color=C1] (12,-44.79) node {$\bullet$};
    \end{tikzpicture}
\end{enumerate}
\end{exercice}

