1. Lesson 13 – 6 Limits of Sequences
Pg #1–16 all, 18, 20, 22–27 all, 30, 32, 34–36
Lesson 13 – 6 Limits of Sequences
Pre-calculus
Objective: Is a sequence CONVergent or divergent?

2. We have looked at sequences, writing them out, summing them, etc.
But, now let’s examine what they “go to” as n gets larger and larger without bound.
Consider
What are the terms going to? Pick a bigger number.
Looks like they get close to 0. So, we say
*Note: There is no term that IS 0, it just gets SUPER CLOSE to 0!

3. To find the limit of a sequence, we usually have to algebraically manipulate it.
Ex 1) Find the limit of a sequence as n increases without bound. a) b)
goes to 0

4. If a sequence gets closer to a number, L, as n increases without bound,
it is said to converge and it is a convergent sequence.
If it does not converge, the sequence is said to diverge.
*Note: If it does diverge, it can do so by several ways – getting larger & larger or by oscillating.
Ex 2) Find the first 5 terms and decide if the sequence converges or diverges. a) b)
getting larger  diverges
diverges

5. Ex 3) Determine whether these geometric sequences converge or diverge.
a) b) c) d)
diverge diverge converge converge
Can you generalize these geometric sequences & make a rule for what will converge & what will diverge?
Try On Your Own!
Ex 4) Characterize each sequence as convergent or divergent. If it converges, give the limit.
convergent
convergent n
divergent 1

6. Homework
Pg #1–16 all, 18, 20, 22–27 all, 30, 32, 34–36