Answer
If $\lim\limits_{n\to\infty} |a_n|=0$, then $\lim\limits_{n\to\infty} a_n=0$
Work Step by Step
Here, we have the property of the absolute value: $-|a_n| \leq a_n \leq |a_n|$ for all the values of $n$
consider $\lim\limits_{n\to\infty} |a_n|=0$
Since, $-|a_n| \leq a_n \leq |a_n|$ for all the values of $n$
By the limit laws of sequences, we have $\lim\limits_{n\to\infty} |a_n|=0$; $\lim\limits_{n\to\infty} -|a_n|=-\lim\limits_{n\to\infty} |a_n|=0$
By the squeeze theorem for sequence, we have $\lim\limits_{n\to\infty} a_n=0$
Hence, If $\lim\limits_{n\to\infty} |a_n|=0$, then $\lim\limits_{n\to\infty} a_n=0$