Now, we also have \(a_{n} \leq a\) and \(b \leq b_{n}\) for all \(n \in \mathbb{N}\) (since \(\left\{a_{n}\right\}\) is increasing and \(\left\{b_{n}\right\}\) is decreasing). Then \(b=\lim _{n \right...Now, we also have \(a_{n} \leq a\) and \(b \leq b_{n}\) for all \(n \in \mathbb{N}\) (since \(\left\{a_{n}\right\}\) is increasing and \(\left\{b_{n}\right\}\) is decreasing). Then \(b=\lim _{n \rightarrow \infty} b_{n}=\lim _{n \rightarrow \infty}\left[\left(b_{n}-a_{n}\right)+a_{n}\right]=a\). \[\lim _{n \rightarrow \infty} a_{n}=\infty, \lim _{n \rightarrow \infty} b_{n}=\infty, \text { and } \lim _{n \rightarrow \infty} c_{n}=-\infty\]