Copyright © 2014, 2010, 2007 Pearson Education, Inc.

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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

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

Definition of a Binomial Coefficient  

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

Pascal’s Triangle

A Formula for Expanding Binomials: The Binomial Theorem

Ex. 2: Using the Binomial Theorem Expand:

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

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

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