Let $\left( u _ { n } \right) _ { n \in \mathbb { N } }$ be a sequence such that $u _ { n } \neq 0$ for every natural number $n$. For every natural number $n$, the sequence $\left( v _ { n } \right) _ { n \in \mathbb { N } }$ is defined by $v _ { n } = - \frac { 2 } { u _ { n } }$. IV-A- If $\left( u _ { n } \right) _ { n \in \mathbb { N } }$ is bounded below by $2$, then $\left( v _ { n } \right) _ { n \in \mathbb { N } }$ is bounded below by $-1$. IV-B- If $\left( u _ { n } \right) _ { n \in \mathbb { N } }$ is increasing, then $\left( v _ { n } \right) _ { n \in \mathbb { N } }$ is decreasing. IV-C- If $\left( u _ { n } \right) _ { n \in \mathbb { N } }$ converges, then $\left( v _ { n } \right) _ { n \in \mathbb { N } }$ converges. For each statement, indicate whether it is TRUE or FALSE.
\section*{Exercise IV}
Let $\left( u _ { n } \right) _ { n \in \mathbb { N } }$ be a sequence such that $u _ { n } \neq 0$ for every natural number $n$. For every natural number $n$, the sequence $\left( v _ { n } \right) _ { n \in \mathbb { N } }$ is defined by $v _ { n } = - \frac { 2 } { u _ { n } }$.\\
IV-A- If $\left( u _ { n } \right) _ { n \in \mathbb { N } }$ is bounded below by $2$, then $\left( v _ { n } \right) _ { n \in \mathbb { N } }$ is bounded below by $-1$.\\
IV-B- If $\left( u _ { n } \right) _ { n \in \mathbb { N } }$ is increasing, then $\left( v _ { n } \right) _ { n \in \mathbb { N } }$ is decreasing.\\
IV-C- If $\left( u _ { n } \right) _ { n \in \mathbb { N } }$ converges, then $\left( v _ { n } \right) _ { n \in \mathbb { N } }$ converges.
For each statement, indicate whether it is TRUE or FALSE.