1. Expand and find the answer.

2. Homework:

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

4. Okay, same series with alternating signs…

5. Now alternate the other way…

6. Try Another…

7. Try Another…

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

9. Find the Factorial

10. Find the Factorial:

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

12. 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?

13. Homework: P 798 # 15 – 43 odd, 47, 48 Portfolio due Monday!!!
Test on Friday! 12-1, 12-2, 12-3, 12-5, 12-6

14. Section 12-6: The Binomial Theorem
In this section we will answer…
How can I determine the answer to a binomial raised to a power quickly?

15. Pascal’s Triangle

16. Binomial Expansion

17. Using Pascal’s Triangle for Binomial Expansion:
Find the row which corresponds to your power.
The coefficients will follow that row.
Powers of first term descend.
Powers of the second term ascend.
Hint: The powers in each term will add up to the original power.

18. Let’s Try One…

19. Something Trickier…

20. Okay, Think You’re Smart? Try This!

21. Add a Twist…

22. Word Problem!
If six children are born into the same family, how many of the possible groups of boys and girls have at least two boys?

23. Congratulations!
You have finished Chapter 12!

24. Homework: Portfolio due Monday!!! P 804 #13 – 31 odd, 36 and 37
Chapter 6 TEST!!! On FRIDAY
Sections 12-1 to 12-3, 12-5 and 12-6
Portfolio due Monday!!!