Question: Suppose that \({{a}_{n}},{{b}_{n}},{{c}_{n}}\) are sequences such that \({{a}_{n}}\le {{b}_{n}}\le {{c}_{n}}\) for all n an element of N and such that the \(\underset{n\to \infty }{\mathop{\lim }}\,{{a}_{n}}=\underset{n\to \infty }{\mathop{\lim }}\,{{c}_{n}}=b\). Prove that \(\underset{n\to \infty }{\mathop{\lim }}\,{{b}_{n}}\)