1 / 6

13.6 Limits of Sequences

13.6 Limits of Sequences. 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.

jess
Download Presentation

13.6 Limits of Sequences

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 13.6 Limits of Sequences

  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 SUPERCLOSE 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 convergentsequence. 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 1.5 1.75 2.3 2.8

  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. 0 convergent convergent n 0 0 divergent 0 1

  6. Homework #1306 Pg 718 #1–16 all, 18, 20, 22–27 all, 30, 32, 34–36

More Related