1. Warm-up p 218 #3, 5, 7 and 9

2. Section 12-5: Sigma Notation and the n th Term In this section we will answer…  What notation can be used to indicate the summation of a series?  How can I expand sigma notation?  How can I build sigma notation from terms?

3.  An auditorium has 10 seats in the 1 st row. Each row has 2 more seats than the one in front of it.  Set up the sequence.  What type of sequence is this?  How many seats in the 10 th row?  How many seats in the n th row?  How many seats in the theater if there 15 rows total?

4. Sigma Notation: A New Way to Write Sums  The series 10 + 12 + 14 +….+ 38 represents the number of seats in the 15 row theater.

5. Sigma Notation: A New Way to Write Sums  The series 10 + 12 + 14 +….+ 38 represents the number of seats in the 15 row theater.  In mathematics, the Greek letter sigma is often used to indicate a sum or series.

6. Sigma Notation This is read: “The sum of 2n + 8 with n from 1 to 15.” For our series:

7. Expanding Sigma Notation

9. Expressing a Series Using Sigma Notation 1.Find d. 2.Find n. 3.Find a n. This will give you the expression for sigma notation. 4.Write in sigma notation.

10. Okay, same series with alternating signs…

11. Now alternate the other way…

12. Try Another…

14. A New Kind of Series… We have learned about arithmetic and geometric series, now meet the Factorial.

15. Find the Factorial

17. Find the Factorial:

18. Try One…  Write the following series in sigma notation.

19. Let’s Recap Can we answer these now?  What notation can be used to indicate the summation of a series?  How can I expand sigma notation?  How can I build sigma notation from terms?

20. Homework:  P 798 # 1 – 43, 47, 48  Portfolio due Monday!!!  Test on Wednesday! 12-1, 12-2, 12-3, 12-5, 12-6