CHAPTER 1 Knowledge and Technique 1 The First Form of Mathematical Induction 2 The Second Form of Mathematicallnduction 3 Well-ordering Principle and Infinite Descent 4 General Terms and Summation of Sequences 5 Arithmetic Sequences and Geometric Sequences 6 Higher-order Arithmetic Sequences and the Method of Differences 7 Recursive Sequences 8 Periodic Sequences Exercise Set 1 CHAPTER 2 Selected Topical Discussions 9 The Fibonacci Sequence 10 Several Proofs of AM-GM Inequality 11 Choosing a Proper Span 12 Choosing the Appropriate Object for Induction 13 Make Appropriate Changes to the Propositions 14 Guessing Before Proving 15 Problems Regarding Existence with Sequences Exercise Set 2 Solutions to Exercises Solutions to Exercise Set 1 Solutions to Exercise Set 2 Bibliography
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