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Binomial Theorem 11.7.

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Presentation on theme: "Binomial Theorem 11.7."— Presentation transcript:

1 Binomial Theorem 11.7

2 Binomial Expansion of the form (a+b)n
There are n+1 terms Functions of n Exponent of a in first term Exponent of b in last term Other terms Exponent of a decreases by 1 Exponent of b increases by 1 Sum of exponents in each term is n Coefficients are symmetric (Pascal’sTriangle) At Beginning--increase Towards End---decrease

3 Expanding Binomials What if the term in a series is not a constant, but a binomial?

4 Pascal’s Triangle The coefficients form a pattern, usually displayed in a triangle Pascal’s Triangle: binomial expansion used to find the possible number of sequences for a binomial pattern features start and end w/ 1 coeff is the sum of the two coeff above it in the previous row symmetric

5 Ex 1 Expand using Pascal’s Triangle

6 Ex 2 Expand using Pascal’s Triangle

7 Binomial Theorem The coefficients can be written in terms of the previous coefficients

8 Ex 3 Expand using the binomial theorem

9 Ex 4 Expand using the binomial theorem

10 Factorials! factorial: a special product that starts with the indicated value and has consecutive descending factors Ex 5 Evaluate

11 Binomial Theorem, factorial form and Sigma Notation

12 Ex 6 Expand using factorial form

13 Ex 6 Expand using factorial form

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