Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 Chapter 10 Additional Topics in Algebra.

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Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 Chapter 10 Additional Topics in Algebra

10 Additional Topics in Algebra Chapter Outline 10.1Sequences and Series 10.2Arithmetic Series 10.3Geometric Series 10.4Mathematical Induction 10.5Counting Techniques 10.6Introduction to Probability 10.7The Binomial Theorem 1-2 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Learning Objectives In Section 10.1 you will learn how to:  A.Write out the terms of a sequence given the general or nth term  B.Work with recursive sequences and sequences involving factorial  C.Find the partial sum of a series  D.Use summation notation to write and evaluate series  E.Use sequences to solve applied problems 10.1 Sequences and Series 1-3 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Learning Objectives In Section 10.2 you will learn how to:  A.Identify an arithmetic sequence and its common difference  B.Find the nth term of an arithmetic sequence  C.Find the nth partial sum of an arithmetic sequence  D.Solve applications involving arithmetic sequences 10.2 Arithmetic Series 1-18 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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1-25 EXAMPLE 5 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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1-29 EXAMPLE 7 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Learning Objectives In Section 10.3 you will learn how to:  A.Identify a geometric series and its common ratio  B.Find the nth term of a geometric sequence  C.Find the nth partial sum of a geometric sequence  D.Find the sum of an infinite geometric series  E.Solve applications involving geometric sequences and series 10.3 Geometric Series 1-30 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Learning Objectives In Section 10.4 you will learn how to:  A.Use subscript notation to evaluate and compose functions  B.Apply the principle of mathematical induction to sum formulas involving natural numbers  C.Apply the principle of mathematical induction to general statements involving natural numbers 10.4 Mathematical Induction 1-47 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Learning Objectives In Section 10.5 you will learn how to:  A.Count possibilities using lists and tree diagrams  B.Count possibilities using the fundamental principle of counting  C.Quick-count distinguishable permutations  D.Quick-count nondistinguishable permutations  E.Quick-count using combinations 10.5 Counting Techniques 1-60 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Learning Objectives In Section 10.6 you will learn how to:  A.Define an event on a sample space  B.Compute elementary probabilities  C.Use certain properties of probability  D.Compute probabilities using quick-counting techniques  E.Compute probabilities involving nonexclusive events 10.6 Introduction to Probability 1-75 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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1-91 EXAMPLE 9B CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Learning Objectives In Section 10.7 you will learn how to:  A.Using Pascal’s Triangle to find (a + b) n  B.Find binomial coefficients using notation  C.Use the binomial theorem to find (a + b) n  D.Find a specific term of a binomial expansion 10.7 The Binomial Theorem 1-92 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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1-105 EXAMPLE 8 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.