Presentation on theme: "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."— Presentation transcript:
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 *Note: There is no term that IS 0, it just gets SUPER CLOSE to 0!
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
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 1.5 1.75 2.3 2.8
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 divergent n 00 1 0
Homework #1306 Pg 718 #1–16 all, 18, 20, 22–27 all, 30, 32, 34–36