# PreCalc Chapter 9

Ch 9 Sequences, Series and Probability

Ch 9.1 Infinite Sequences and Summation Notation

Introduction to Sequences ;
Finding the First  Terms of  ;
Finding the First  Terms of  ;
Finding the Terms of Reclusive Defined Infinite Sequence ;  ;
Finding the Terms of Reclusive Defined Infinite Sequence ; ,  ;
Finding the Common Difference of Infinite Sequence  ;
Finding the Common Difference of Sequence

Definition of Summation Notation ;
Finding  ;
Finding  ;
Finding  ;
Finding

Ch 9.2 Arithmetic Sequences

Definitions of , , , and  in Arithmetic Sequences ;
Given the Arithmetic Sequence , determining , and determining which Term in the Sequence has the Value of  (Part 1)

Given the Arithmetic Sequence , determining , and determining which Term in the Sequence that has the Value of  (Part 2) ;
Writing the First  Terms of the Arithmetic Sequence given   and  ;
Finding  of the Arithmetic Sequence given  and

Definitions of , , ,  and  in Arithmetic Series ;
Determining the Sum of the First  Terms of the Arithmetic Series  ;
Determining  of the Arithmetic Series given  and  ;
Determining the First  Terms of the Arithmetic Series given , , and  ;
Determining the Number of Cans in a Trapezoid (Part 1)

Determining the Number of Cans in a Trapezoid (Part 2)

Ch 9.3 Geometric Sequences

Definitions of and Terms used in Geometric Sequence ;
Determining the  Term, and Determining if the Geometric Sequence  is Convergent or Divergent ;
Creating a Geometric Sequence whose  Term is  ;
In a Finite Geometric Sequence given  and , determining  and  and determining the Numbers of Terms if the Last Term is  (Part 1)

In a Finite Geometric Sequence given  and , determining  and   and determining the Numbers of Terms if the Last Term is  (Part 2)

Definitions of and Terms used in Geometric Series ;
Determining the Sum of the First  Terms for the Geometric Series  ;
Determining the  Term of the Geometric Series given the Sum of the First  Terms is  and the Common Ratio is  ;
Finding the Sum of the Geometric Series  ;
Discussing why the “Sum of  Terms of a Geometric Series” Formula also be Written as
where

Definitions of and Terms used in Infinite Geometric Series ;
Determining whether the Infinite Geometric Series  has a Finite Sum, and Estimating it ;
Determining whether the Infinite Geometric Series  has a Finite Sum, and Estimating it ;
Determining whether the Infinite Geometric Series  has a Finite Sum, and Estimating it ;
Determining whether the Infinite Geometric Series  Converges or Diverges and Determining its Sum if it Converges ;
Determining whether the Infinite Geometric Series  Converges or Diverges and Determining its Sum if it Converges ;
Determining a Fraction that is Equal to  (Part 1)

Determining a Fraction that is Equal to  (Part 2)

Definitions of and Terms used in Sigma Notation ;
Finding the Sum of  ;
Finding the Sum of  ;
Finding the Sum of  ;
Expressing the Sum in terms of Summation Notation for the Series  ;
Expressing the Sum in terms of Summation Notation for the Series

Ch 9.5 The Binomial Theorem

Evaluating  ,  ,  ,  ,  ,  ,  http://www.youtube.com/watch?feature=player_embedded&v=4j66DS_XTSo

Finding Binomial Coefficient of  ;
Finding Binomial Coefficient of

Introducing the Binomial Theorem ;
Finding a Binomial Expansion of  ;
Finding a Binomial Expansion of

Finding a Binomial Expansion of

Ch 9.6 Permutations

Definition of Permutation ;
Listing the Numbers of Different Ways  Students can Line up to Purchase a New Textbook Reader ;
Definition of -Factorial ;
Determining  And  ;
Definition of Permutation of  Items  at a Time ;
Finding the Permutations of  ,  ;
Finding the Number of Different Arrangements of Students Giving a Presentation to the Class ;
Finding the Number of Different Ways the Letter of Word PHOENIX can be Arranged

Finding the Permutations of  ,  ,  ;
Finding the Number of Different Ways to Put  Horses for the First Place, the Second Place and the Third Place in a Horse Run ;
Finding the Number of Different Ways for a Class President and Class Vice President from  Students ;
Finding the Number of Different Batting Orders for a Team of Every of  Baseball Players

Ch 9.7 Distinguishable Permutations and Combinations

Definition of Distinguishable Permutation ;
Finding the Number of Ways the Letter of Word MATHEMETICS can be Arranged ;
Finding the Number of Ways to Order  Blue Marbles,  Red Marbles and  Green Marbles
http://www.youtube.com/watch?v=JyRKTesp6fQ (Last Three Parts of the Video)

Definition of Combination ;
Finding the Number of Committees of  can be Formed from a Group of  Students ;
Definition of Combinations of  Items Taken   at a time ;
Finding the Combinations of  ,  ;
Finding the Number of Different Groups of Players can be on the Field at One Time ;
Finding the Number of Ways a Student can Take  Classes Next Semester for  Classed Needed ;
Finding the Number of Different Groups can be Formed from the Office