**Lemma** If $a_{n} \to a$ then $|a_{n}| \to |a|$ **Proof** Using [[Reverse triangle inequality]], $||a_{n}|-|a|| \leq |a_{n}- a|$Given any $\epsilon>0$, choose $N$ such that $|a_{n}-a|<\epsilon$ for all $n \geq N$; then $||a_{n}|-|a_{n}||< \epsilon$ for all $n \geq N$ too. $\square$