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