#### Answer

FALSE

#### Work Step by Step

'Test for Divergence' Theorem states that if $\lim\limits_{n \to \infty}a_{n}$ does not exist or does not equal zero then the series is divergent.
If a series is convergent the limit is always zero. But it does not necessarily mean that if the limit of a series is zero that it is convergent.
Hence, the statement is false.