1. Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Chapter 11
Sequences, Induction, and Probability
11.5 The Binomial Theorem
Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1

2. Objectives:
Evaluate a binomial coefficient.
Expand a binomial raised to a power.
Find a particular term in a binomial expansion.

3. Definition of a Binomial Coefficient

5. Ex. 1: Evaluating Binomial Coefficients
Evaluate each of the following:

6. Pascal’s Triangle

7. A Formula for Expanding Binomials: The Binomial Theorem

8. Ex. 2: Using the Binomial Theorem
Expand:

9. Finding a Particular Term in a Binomial Expansion
The (r + 1)st term of the expansion of (a + b)n is

10. Ex 3: Finding a Single Term of a Binomial Expansion
Find the fifth term in the expansion of