A sequence is called convergent if its limit is finite, and divergent if its limit is infinite (either +∞ or -∞). The difference between these two type of sequences will be discussed in this page.
Convergent and Divergent Sequence Difference
The differences of convergent and divergent sequences are listed in the table below.
| Convergent Squence | Divergent Sequence |
| A sequence {xn} is called convergent if its limit is finite. | A sequence {xn} is called divergent if its limit is infinite, either +∞ or -∞. |
| limn→∞ xn = finite. | limn→∞ xn = +∞ or -∞. |
| {1/n} is an example of a convergent sequence with limit 0. That is, limn→∞ 1/n = 0. | {n} is an example of a divergent sequence with limit +∞. That is, limn→∞ n = +∞. |
| The terms of a convergent sequence continuously approaches to a specific finite value (the limit). | The terms of a divergent sequence may rises without bound (towards +∞) or decreases without bound (towards -∞). |
| The graph of a convergent sequence flattens out near a specific horizontal line (the limit). | The graph of a divergent sequence may continuously rise or fall. |
Also Read:
- A Convergent Sequence is Bounded: Proof, Converse
- Convergent Sequence: Definition and Examples
- Divergent Sequence: Definition, Examples
- Bounded sequence definition examples
- Unbounded sequence definition examples
FAQs
Q1: What are the differences between convergent and divergence sequences?
Answer: Convergent sequence has finite limit where as divergent sequence has infinite limit. For example, {1/n} is a convergent sequence and {n} is a divergent sequence.