Let [math]\left\{a_n\right\}[/math], [math]\left\{b_n\right\}[/math], and [math]\left\{c_n\right\}[/math] be sequences of real numbers. If [math]a_n\le b_n\le c_n[/math] for all [math]n[/math] beyond some index [math]N[/math], and if [math]\text{lim}_{n\longrightarrow\infty}a_n=\text{lim}_{n\longrightarrow\infty}c_n=L[/math], then [math]\text{lim}_{n\longrightarrow\infty}b_n=L[/math].

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]