**Lemma** If $a_{n} \to \infty$ as $n \to \infty$ then $\frac{1}{a_{n}} \to 0$ as $n \to \infty$ **Proof** Given $\epsilon>0$, since $a_{n} \to \infty$ there exists $N$ such that $a_{n}> \frac{1}{\epsilon}$ for all $n \geq N$. Then $0\leq \frac{1}{a_{n}}< \epsilon \implies \left \lvert \frac{1}{a_{n}} \right \rvert < \epsilon$for all $n \geq N$ and so $a_{n} \to 0$ as $n \to \infty$.