A sequence \u201can\u201d 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.<\/p>\n
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.<\/p>\n
For example, a sequence ((-1)^n)\/n has a list of elements {-1, 1\/2, -1\/3, 1\/4, -1\/5\u2026}. 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.<\/p>\n
For a divergent sequence example, we can have a sequence (-1)^n, which has a list of elements {-1, 1, -1, 1, -1, 1\u2026}. Observably, it is not going to get close to one specific number. So, this sequence is divergent.<\/p>\n","protected":false},"excerpt":{"rendered":"
A sequence \u201can\u201d 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 … Continue reading What distinguishes convergent sequences from divergent sequences?<\/span>