13 4 limits of infinite sequences

Objectives:

1. Find or estimate limits of infinite

sequences

Investigating LimitsLet’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:

Another ExampleNow, let’s look at:

tn gets closer and

closer to 1, so

we say:

Estimating LimitsYou can often estimate the limit of an

infinite sequence by plugging in large

values for n.

Example:

Find

ExampleFind

TheoremIf |r| < 1, then

Another MethodFor limits of rational expressions:

Look at highest degree term on top

and bottom

Usually the first term

Compare degrees, then use these

rules…

If degrees are equal:

limit = ratio of coefficients

Example:

If top degree is higher:

limit = ∞

Example:

If bottom degree is higher:

limit = 0

Example:

You Try!

“The Limit Does Not Exist”If the terms do not approach any

certain value, the sequence has no

limit.

Ex:

does not exist

You Try!Find the limit of each sequence:

1, -4, 9, -16, 25, -36, …