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.
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