Q1: For any integer n, let An=[1/(2^n*root5)] *[(1+root5)^n-(1-root5)^n] ;
Bn=1/2 *[(1+root5)^n+(1-root5)^n]. Prove by induction that An,Bn are integers. Deduce that [1/(2^n*root5)] *[(1+root5)^2n-(1-root5)^2n] is even.
Q2: guess and prove a formula for tan^-1 (1/n)-tan^-1(1/n+1).
pure maths MI
2009-02-15 10:55 pm
回答 (2)
2009-02-16 12:47 am
✔ 最佳答案
Please refer to the following links.http://i718.photobucket.com/albums/ww188/physicsworld2009/physicsworld05Feb151645.jpg
http://i718.photobucket.com/albums/ww188/physicsworld2009/physicsworld06Feb151645.jpg
http://i718.photobucket.com/albums/ww188/physicsworld2009/physicsworld07Feb151645.jpg
參考: physics king
2009-02-17 4:39 am
question for An, why (1/2)*N+(1/2^k)*M is an integer???
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https://hk.answers.yahoo.com/question/index?qid=20090215000051KK01055