Sort these infinite sequences into groups.
- How will you choose to define the groups?
- Are there some sequences which belong to more than one group?
When looking for ways to group the sequences you might ask yourself the following questions.
Is each term bigger or smaller than the previous one?
How does the difference between adjacent terms change as you go along the sequence?
Thinking about a pair of sequences, what is the same and what is different?
Can you find a rule for generating the \(n^\text{th}\) term?
You might find it helpful to plot a graph of a sequence to get a feel for how it is behaving.
