# How do you determine whether the infinite sequence a_n=(-1)^n converges or diverges?

${\left\{{a}_{n}\right\}}_{n = 1}^{\infty} = \left\{- 1 , + 1 , - 1 , + 1 , \ldots\right\}$
It simply alternates between -1 and +1, so it does not approach any single finite value; therefore, ${\lim}_{n \rightarrow \infty} {a}_{n}$ does not exist, which means that the sequence diverges.