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Pre-Cal 40S Slides December 5, 2007

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More on the binomial theorem.

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Pre-Cal 40S Slides December 5, 2007

1. 1. The Fibonacci Sequence and the Binomial Theorem ... Sunflower
2. 2. Pascal's Triangle How many different patterns can you find in the triangle?
3. 3. Pascal's Triangle Can you find the Fibonacci sequence in the triangle?
4. 4. 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
5. 5. Recall: This relation holds for each term in any binomial expansion: [exponent on a] + [exponent on b] = n And any individual term in a binomial expansion can be represented like this: Example: Find the term that contains x in the expansion of
6. 6. Recall: This relation holds for each term in any binomial expansion: [exponent on a] + [exponent on b] = n And any individual term in a binomial expansion can be represented like this: Example: Find the term that contains x in the expansion of
7. 7. Recall: This relation holds for each term in any binomial expansion: [exponent on a] + [exponent on b] = n And any individual term in a binomial expansion can be represented like this: Example: Find the term that contains x in the expansion of
8. 8. Example: Find the term that contains x7 in the expansion of
9. 9. Determine the indicated term in each expansion. (a) the 8th term in the expansion of
10. 10. Determine the indicated term in each expansion. (b) the 4th term in the expansion of
11. 11. Determine the indicated term in each expansion. (c) the middle term in the expansion of
12. 12. Find the term that contains in the expansion of: This question is HOMEWORK and Exercise #34.