Chap 3. Exercise 1

Prove that \(\{s_n\}\) converges implies that \(\{|s_n|\}\) converges. Is the converse true?

Suppose \(\lim\limits_{n\to\infty}s_n=s\).
\(\forall \varepsilon>0,\exists N\in\mathbb{N}^+\) such that \(n>N\) implies \(||s_n|-|s||<|s_n-s|<\varepsilon\). Therefore \(\{|s_n|\}\) converges to \(|s|\).