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Binomial Theorem

Binomial Theorem. 11.7. 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 )

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Binomial Theorem

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  1. Binomial Theorem 11.7

  2. 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 Binomial Expansion of the form (a+b)n

  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 or

  12. Ex 6 Expand using factorial form

  13. Ex 6 Expand using factorial form

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