\( \newcommand{\matr}[1] {\mathbf{#1}} \newcommand{\vertbar} {\rule[-1ex]{0.5pt}{2.5ex}} \newcommand{\horzbar} {\rule[.5ex]{2.5ex}{0.5pt}} \)
header
Show Answer
\( \newcommand{\cat}[1] {\mathrm{#1}} \newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})} \newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}} \)
Math and science::Analysis::Tao::06. Limits of sequences

Zero test for sequences

A consequence of the squeeze test is the following:

Let \( (a_n)_{n=m}^{\infty} \). Then the limit \( \lim_{n\rightarrow \infty} a_n \) exists and is equal to zero if and only if the limit [...] exists and is equal to zero.