For each of the following statements, indicate whether it is true or false. Each answer must be justified. An unjustified answer earns no points.

\textbf{Statement 1:} Let (E) be the differential equation: $y ^ { \prime } - 2 y = - 6 x + 1$.\\
The function $f$ defined on $\mathbb { R }$ by: $f ( x ) = \mathrm { e } ^ { 2 x } - 6 x + 1$ is a solution of the differential equation (E).

\textbf{Statement 2:} Consider the sequence $\left( u _ { n } \right)$ defined on $\mathbb { N }$ by
$$u _ { n } = 1 + \frac { 3 } { 4 } + \left( \frac { 3 } { 4 } \right) ^ { 2 } + \cdots + \left( \frac { 3 } { 4 } \right) ^ { n }$$
The sequence $(u _ { n })$ has limit $+ \infty$.

\textbf{Statement 3:} Consider the sequence $(u _ { n })$ defined in Statement 2.\\
The instruction suite(50) below, written in Python language, returns $u _ { 50 }$.
\begin{verbatim}
def suite(k):
    S=0
    for i in range(k):
        S=S+(3/4)**k
    return S
\end{verbatim}

\textbf{Statement 4:} Let $a$ be a real number and $f$ the function defined on $] 0 ; + \infty [$ by:
$$f ( x ) = a \ln ( x ) - 2 x$$
Let $C$ be the representative curve of the function $f$ in a coordinate system $(O ; \vec { \imath } , \vec { \jmath })$.\\
There exists a value of $a$ for which the tangent to $C$ at the point with abscissa 1 is parallel to the horizontal axis.