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Pre-Cal 40S Slides December 5, 2007
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Pre-Cal 40S Slides December 5, 2007

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More on the binomial theorem.

More on the binomial theorem.

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  • 1. The Fibonacci Sequence and the Binomial Theorem ... Sunflower
  • 2. Pascal's Triangle How many different patterns can you find in the triangle?
  • 3. Pascal's Triangle Can you find the Fibonacci sequence in the triangle?
  • 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. 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. 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. 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. Example: Find the term that contains x7 in the expansion of
  • 9. Determine the indicated term in each expansion. (a) the 8th term in the expansion of
  • 10. Determine the indicated term in each expansion. (b) the 4th term in the expansion of
  • 11. Determine the indicated term in each expansion. (c) the middle term in the expansion of
  • 12. Find the term that contains in the expansion of: This question is HOMEWORK and Exercise #34.