Section 4 - Slides.notebook - 2012-2013 Algebra 2

Section 4 Slides.notebook

1

September 18, 2012

Gameplan:1. Homework questions (5)2. Concept checklist (10)2. Investigating ininite geometric series (15)3. Partial sums and graphing (15)4. Ininite sums (10)

Homework:

49. 131,070 50. 255/32 51. 1365/256

40. 17545. 315 46. 450 47. 132 48. 161


2

September 18, 2012

Concept Checklist:1. Find the value of n:

2. In a skydiving formation with R rings, each ring after the irst has twice as many as the previous. If there are 5 divers in the irst ring, how many are there in 4 rings?


3

September 18, 2012

Investigation (Page 819)Start with a piece of paper. Its area will be considered 1.

Step 1: Fold the paper in half and cut along the fold. Set one piece aside.

Step 2: Take the other piece and fold it in half and cut along the fold. Set one piece aside.

Step 3: Continue steps 1 and 2 until its too dificult to fold.

Fill in the table:

1. What does the combined area appear to be approaching?

2. Using the formula for the sum of a inite geometric series, write and simplify a rule for the combined area A of the pieces of paper after n cuts. What happens to A as n goes to ininity?


4

September 18, 2012

Another Way (Visual):

1/3

1/9

1/27

1/81

What is the equation of the geometric sequence?

Assuming the square has an area of 1, what does the sum of the infinite geometric series appear to be?

Convergent vs. DivergentAn infinite geometric series is...

Convergent if the sum approaches a finite value.

Divergent if the sum does not approach a finite value.

Just like our observations from the graphing activity, the key is the common ratio!

A limit exists only if the series converges.


5

September 18, 2012

Going back to the problem with the square let's show that the limit really is 1/2:

Find the sum of the infinite geometric series:


6

September 18, 2012

Homework:

Section 4 - Slides.notebook - 2012-2013 Algebra 2

Documents

Transcript of Section 4 - Slides.notebook - 2012-2013 Algebra 2