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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 \( \lim_{n \rightarrow \infty} |a_n| \) exists and is equal to zero.

Proof?