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

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?

 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?

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

Sigma Notation: A New Way to Write Sums  The series ….+ 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.

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

Expanding Sigma Notation

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.

Okay, same series with alternating signs…

Now alternate the other way…

Try Another…

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

Find the Factorial

Find the Factorial:

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

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?

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