In China, lots of excellent maths students takes an active part in
various maths contests and the best six senior high school students will
be selected to form the IMO National Team to compete in the
International Mathematical Olympiad. In the past ten years, China's IMO
Team has achieved outstanding results -- they have won the first place
almost every year.The author is one of the senior coaches of China's IMO
National Team, he is the headmaster of Shanghai senior high school which
is one of the best high schools of China. In the past decade, the
students of this school have won the IMO gold medals almost every
year.The author attempts to use some common characteristics of sequence
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.