If a sequence does not converge, then it is said to diverge or to be a divergent sequence.
For example, the following sequences all diverge, even though they do not all tend to infinity or minus infinity:
\[\begin{align*} &1,\ 2,\ 4,\ 8,\ 16,\ 32,\ \dotsc\\ &1,\ 0,\ 1,\ 0,\ 1,\ 0,\ \dotsc\\ &0,\ 1,\ 0,\ 2,\ 0,\ 4,\ 0,\ 8,\ \dotsc\\ &1,\ {-2},\ 3,\ {-4},\ 5,\ {-6},\ \dotsc\\ \end{align*}\]
