1. Prove by mathematical induction , that (3n+1)x7^n-1 is divisible by 9 for all natural no. n
2. Prove by mathematical induction , that x^n+y^n is divisble by x+y for all positive odd no. n
3. a) Expand (k+3)^3
b) Prove by mathematical induction , that the sum of the cubes of any three
consecutive natural no is divisble by 9.
F.4 A.Maths(Application to Divisibility Problems)(URGENT!!!)
2008-07-06 8:59 pm
回答 (2)
2008-07-06 11:44 pm
✔ 最佳答案
Q1 & 2 :http://hk.knowledge.yahoo.com/question/question?qid=7007102902611
Q3:
圖片參考：http://i238.photobucket.com/albums/ff245/chocolate328154/Maths294.jpg?t=1215330208
2008-07-06 15:46:38 補充：
如有不清楚歡迎提出, 但請不要移除問題, thx!
2008-07-06 18:01:19 補充：
係呀, 打錯少少嘢, 更正:
When n = k + 2 ,
x^2 ( x^ k ) + y^2 ( y^k )
= x^2 ( x^k + y^k ) - x^2 ( y^k ) + y^2 ( y^k )
= Mx^2 ( x + y ) - y^k ( x + y )( x - y )
= ( x + y )[ Mx^2 - ( y^k )( x - y )]
So P ( k + 2 ) is true.
參考: My Maths Knowledge
2008-07-07 12:49 am
第二題我覺得最後應該係
= ( x + y )[ M*x^2 – ( y^k )( x – y ) ]
= ( x + y )[ M*x^2 – ( y^k )( x – y ) ]
收錄日期: 2021-04-16 22:48:27
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080706000051KK00962