What does it mean to say that $u_{n} \rightarrow l$ as $n \rightarrow \infty$ ?

Show that, if $u_{n} \rightarrow l$ and $v_{n} \rightarrow k$, then $u_{n} v_{n} \rightarrow l k$ as $n \rightarrow \infty$.

If further $u_{n} \neq 0$ for all $n$ and $l \neq 0$, show that $1 / u_{n} \rightarrow 1 / l$ as $n \rightarrow \infty$.

Give an example to show that the non-vanishing of $u_{n}$ for all $n$ need not imply the non-vanishing of $l$.