Notes 9.2 – The Binomial Theorem

I. Alternate Notation A.) Permutations – None B.) Combinations -

II. Pascal’s Triangle A.) A triangular array of the coefficients of the binomial coefficients of a and b in the expansion of where n = 0 is the top row.

B.) Recursion Formula for the n th row of Pascal’s Triangle - The n th row of Pascal’s Triangle = C.) Ex. 1 - Determine the 6 th row of Pascal’s Triangle

III. The Binomial Theorem A.) Thm.: for any positive integer n, where

B.) Ex. 2 - Expand

C.) Ex. 3 - Find the term of D.) Ex. 4 - Find the sum of the coefficients of E.) Thm.: - The sum of the coefficients of

E.) Prove for all n ≥ 2.