Science:Infinite Series Module/Units/Unit 1/1.1 Infinite Sequences/1.1.09 Squeeze Theorem For Sequences

The Squeeze Theorem for functions can also be adapted for infinite sequences.

Theorem: Squeeze Theorem for Infinite Sequences
Suppose $a_{n}\leq b_{n}\leq c_{n}$ for $n\geq n_{0}$ and $\lim _{n\rightarrow \infty }a_{n}=\lim _{n\rightarrow \infty }c_{n}=L,$ then $\lim _{n\rightarrow \infty }b_{n}=L.$

This theorem allows us to evaluate limits that are hard to evaluate, by establishing a relationship to other limits that we can easily evaluate. Let's see this in an example.