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 $$c_n \rightarrow L$$.