\( a _ { n } ) : 1 , \frac { 1 } { 1 + 2 } , \frac { 1 } { 1 + 2 + 3 } , \cdots , \frac { 1 } { 1 + 2 + 3 + \cdots + n } \)

\begin{tabular}{|l|}\hline Considérons la suite \( \left(U_{n}\right) \) définie par: \( U_{0}=15 \) et \\ ( \( \forall n \in \mathbb{N})=U_{n+1}=\frac{7}{5} U_{n}-5 \) et \( \left(V_{n}\right) \) la suite définie \\ par: \( (\forall n \in \mathbb{N})=V_{n}=U_{n+1}-U_{n} \). \\ 1. Montrer que la suite \( \left(V_{n}\right) \) est géométrique dont \\ \( \quad \) on déterminera la raison. \\ 2. Déterminer \( V_{n} \) en fonction de \( n \). \\ 3. On pose \( S_{n}=\sum_{i=0}^{i=n} V_{i}=V_{0}+V_{1}+\cdots+V_{n} \). \\ 3.1. Montrer que \( (\forall n \in N): S_{n}=U_{n+1}-U_{0} \). \\ 3.2. En déduire \( U_{n} \) en fonction den. \\ \hline\end{tabular}

5. \( \forall \alpha \in \mathbb{R} \) için, \( A=-2 \sin \alpha+1 \) olduğuna göre, A nın değer aralığı nedir?

3-Determine the domain of \( f(x, y)=\sqrt{x^{2}-9}-\ln (y-1) \) \[ \begin{array}{ll}\text { (a) }|x| \geq 3 \text { and } y>1 & \text { (b) }|x| \leq 3 \\ \text { (c) }|x| \geq 3 \text { and } y=1 & \end{array} \]

Identify the trace of the surface \( 3 x+2 x^{2}-z^{2}-2 y=5 \) on \( y z \)-plase \( \begin{array}{llll}\text { A. Ellipse } & \text { (B) Circle } & \text { C. Hyperbola } & \text { D. Par }\end{array} \)

Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \) Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s).