Pre-Cal 40S May 12, 2009

481 views
434 views

Published on

Working with the binomial theorem.

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
481
On SlideShare
0
From Embeds
0
Number of Embeds
60
Actions
Shares
0
Downloads
9
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Pre-Cal 40S May 12, 2009

  1. 1. Poker Combinatorics or How likely is THAT?!? Red Hot Poker by flickr user kimberlyfaye
  2. 2. The Binomial Theorem ... Algebraically Combinatorically Notice the patterns ... (1) The coefficient of the term is: (2) The exponent on a is given by: [n - (i - 1)] (3) The exponent on b is given by: i - 1 (4) This relation holds for each term in the expansion: [exponent on a] + [exponent on b] = n (5) The number of terms in any binomial expansion is: n + 1
  3. 3. Evaluate each term ... n! nC r = (n-r)!r!
  4. 4. Pascal's Triangle Can you find the Hockey Stick pattern?
  5. 5. Any individual term, let's say the ith term, in a binomial expansion can be represented like this: Example: Find the 4th term in the expansion of
  6. 6. Determine the indicated term in each expansion. (a) the 8th term in the expansion of
  7. 7. Example: Find the term that contains x7 in the expansion of
  8. 8. Find the term that contains in the expansion of:
  9. 9. Find the term that contains in the expansion of:

×