世界数学奥林匹克经典：数列与数学归纳法 第2版

　　Mathematical induction is an important method used to prove particular math statements and is widely applicable in different branches of mathematics， among which it is most frequently used in sequences.This book is rewritten on the basis of the book Methods and Techniques for Proving by Mathematical Induction ， and is written with an understanding that sequences and mathematical induction overlap and share similar ideas in the realm of mathematics knowledge. Since there are a lot of theses and books related to this topic already， the author spent quite a lot of time reviewing and refining the contents in order to avoid regurgitating information. For example， this book refers to some of the most updated Math Olympiad problems from different countries， places emphasis on the methods and techniques for dealing with problems， and discusses the connotations and the essence of mathematical induction in different contexts.The author attempts to use some common characteristics of sequences and mathematical induction to fundamentally connect Math Olympiad problems to particular branches of mathematics. In doing so. the author hopes to reveal the beauty and joy involved with math exploration and at the same time， attempts to arouse readers' interest of learning math and invigorate their courage to challenge themselves with difficult problems.

　　作者简介冯志刚，国家督学，享受国务院政府特殊津贴专家。上海中学校长，上海市特级教师、正高级教师，上海市名教师基地主持人，上海市数学会副理事长。1969年4月生，1990年从华东师范大学数学系毕业后，在上海中学工作至今，长期从事数学奥林匹克教学工作。教过的学生中，有超过100人次进入中国数学奥林匹克国家集训队，其中有12人次获得IMO金牌，曾连续9年有学生获得IMO金牌。热心数学奥林匹克普及工作，是中国西部数学邀请赛执委会委员，曾5次出任IMO中国国家队副领队，数次担任罗马尼亚大师杯数学奥林匹克（RMM）中国队副领队、领队。

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