A sequence “an” is a list of elements that have its own order to follow with an increasing in positive integer number n. If we want to consider a sequence is convergent or divergent, we need to look at the tendency of the elements as n goes to infinity.

As long as the elements is getting closer and closer to one specific number, while n is approaching to infinity, then we can say this sequence is convergent. Otherwise, the sequences are divergent.

For example, a sequence ((-1)^n)/n has a list of elements {-1, 1/2, -1/3, 1/4, -1/5…}. We can see that although elements are jumping back and forth between the x-axis, as n gets as large as we need, this sequence is as close as we want to 0. That is, the sequence is convergent.

For a divergent sequence example, we can have a sequence (-1)^n, which has a list of elements {-1, 1, -1, 1, -1, 1…}. Observably, it is not going to get close to one specific number. So, this sequence is divergent.