Convergence of Infinite Sequences Example

Previous: Convergence of Infinite Sequences


Next: Relationship to Limits of Functions




Example

Determine whether the sequences

and converge.

Complete Solution

The Sequence an

Using the definition of convergence of an infinite sequence, we would evaluate the following limit:

Because this limit evaluates to a single finite number, the sequence converges.

The Sequence bn

While the sequence an converges to 1/2, bn does not converge because its terms do not approach any number. Instead, the terms in the sequence oscillate between -1 and +1.

The sequence bn does not converge to a unique number, and so bn does not converge.


Previous: Convergence of Infinite Sequences


Next: Relationship to Limits of Functions



Leave a Reply

Your email address will not be published. Required fields are marked *