Pre-Cal 40S Slides April 25, 2007
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Introduction to the Binomial Theorem.
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Pre-Cal 40S Slides April 25, 2007
- 1. The Binomial Theorem or "one of the ways G-d built the universe" ... Zhu Shijiei 1261 Pascal 1653
- 2. Expand and simplify ... a+b
- 3. Find a pattern, add two more rows to the triangle ... 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1
- 4. Evaluate each term ...
- 5. Pascal's Triangle How many different patterns can you find in the triangle? SYMMETRY Counting Numbers Sum of COUNTING numbers triangular numbers Sum of Triangular numbers
- 6. Pascal's Triangle How many different patterns can you find in the triangle?
- 7. Pascal's Triangle How many different patterns can you find in the triangle?
- 9. 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 (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