Proof of the Squeeze Theorem for limits of sequences:

Let \({a_n}\), \({b_n}\), and \({c_n}\) be sequences such that \(a_n \le b_n \le c_n\) for \(n \gg 1\). Suppose that \(a_n \rightarrow L\) and \(c_n \rightarrow L\).

Let \({a_n}\), \({b_n}\), and \({c_n}\) be sequences such that \(a_n \le b_n \le c_n\) for \(n \gg 1\). Suppose that \(a_n \rightarrow L\) and \(c_n \rightarrow L\).