Let $\{a_n\}$ be a sequnce. Then $a_n \to -\infty$ if $\forall K < 0 \;\exists N \;\forall n \ge N:a_n < K$
Show that:
If $a_n → -\infty$, $a_n \ne 0$, then $1/a_n→0$ ; and
If $a_n < 0$, $a_n → 0$, then $1/a_n→−∞$
From the highschool I know that this is true. But do not know how to prove it. Can you help me?