1. Objectives:
1. Find or estimate limits of infinite
sequences

2. Investigating Limits
Let’s take this infinite geometric
sequence:
t10 ≈ 0.001
t50 ≈ 0.000000000000000001
So, since tn is approaching 0 as n gets
really big, we say:

3. Another Example
Now, let’s look at:
tn gets closer and
closer to 1, so
we say:

4. Estimating Limits
You can often estimate the limit of an
infinite sequence by plugging in large
values for n.
Example:
Find

5. Example
Find

6. Theorem
If |r| < 1, then

7. Another Method
For limits of rational expressions:
Look at highest degree term on top
and bottom
 Usually the first term
Compare degrees, then use these
rules…

8. If degrees are equal:
 limit = ratio of coefficients
Example:

9. If top degree is higher:
 limit = ∞
Example:

10. If bottom degree is higher:
 limit = 0
Example:

11. You Try!



12. “The Limit Does Not Exist”
If the terms do not approach any
certain value, the sequence has no
limit.
Ex:
does not exist

13. You Try!
Find the limit of each sequence:

1, -4, 9, -16, 25, -36, …