Prove that if $\lim_{n\to \infty} a_n=\infty$ then $\lim_{n\to \infty} \frac{1}{a_n}=0$

Question

let $C= \frac{1}{\epsilon}$

There $\exists N\in\mathbb N$ such that for every $n>N$, it is true that: $$a_n>\frac{1}{\epsilon}$$

We should prove that for every $\epsilon>0$ there exists such a $N\in\mathbb N$, for every $n>N$ $$\left|\frac1{a_n}\right|<\epsilon$$

So we take the N that satisfies the first conclusion, and that will mean for every $n>N$$$\left|\frac1{a_n}\right|<\epsilon$$