Answer:

When the terms of a sequence of numbers grow so that there is no upper bound to their size, the sequence is said to diverge.

For example, 1, 2, 4, 8, 16, 32 … diverges, However 1/2, 3/4, 7/8, 15/16, 31/32 …. Does not diverge. Its terms although increasing, never exceeded 1. This sequence is said to converge to 1.