For each of the following statements, specify whether it is true or false then justify the answer given. Any answer without justification will not be taken into account.

\begin{enumerate}
  \item Statement 1: Any decreasing sequence and bounded below by 0 converges to 0.
  \item We consider a sequence $(u_n)$ defined on $\mathbb{N}$ such that, for every integer $n$, we have
$$u_n \leq \frac{-9^n + 3^n}{7^n}.$$
Statement 2: $\lim_{n \rightarrow +\infty} u_n = -\infty$.
  \item We consider the following function written in Python language:
\begin{verbatim}
def terme(N) :
    U = 1
    for i in range(N) :
        U = U + i
    return U
\end{verbatim}
Statement 3: terme(4) returns the value 7.
  \item During a competition, the winner has a choice between two prizes:
\begin{itemize}
  \item Prize A: they receive 1000 euros per day for 15 days;
  \item Prize B: they receive 1 euro on day 1, 2 euros on day 2, 4 euros on day 3 and for 15 days the sum received doubles each day.
\end{itemize}
Statement 4: The value of prize A is higher than the value of prize B.
  \item We consider the sequence $(v_n)$ defined for every integer $n \geq 1$ by
$$v_n = \int_1^n \ln x \mathrm{~d}x.$$
Statement 5: The sequence $(v_n)$ is increasing.
\end{enumerate}