Science:Infinite Series Module/Units/Unit 1/1.1 Infinite Sequences/1.1.03 Convergence of Infinite Sequences Example

From UBC Wiki
Jump to navigation Jump to search


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.