中4,A-MATHS問題(10大分)

2008-09-07 4:20 am
呢條唔識做...

利用數學歸納法,證明對於所有正正數n,下列各命題都成立!




 1     1     1            
-----+-----+-----+.......    1.3.5 3.5.7 5.7.9 


     1        n(n+2)
+--------- = -------
(2n-1)(2n+1)(2n+3)    3(2n+1)(2n+3)


呢課係數學歸納法

做得詳細d,,十萬個唔該晒!!
更新1:

1 1 1 1 n(n+2) _________+________+________+________________ = ____________ 1X3X5 3X5X7 5X7X9 (2n-1)(2n+1)(2n+3) 3(2n+1)(2n+3) 睇呢到睇得清楚d

回答 (2)

2008-09-07 6:24 am
✔ 最佳答案
Explanation as follows:

圖片參考:http://i238.photobucket.com/albums/ff245/chocolate328154/Maths455.jpg?t=1220711072
參考: My Maths Knowledge
2008-09-07 6:29 am
1/(1*3*5) 1/(3*5*7) ...... 1/[(2n-1)*(2n 1)*(2n 3)]

={1/(1*3)-1/[(2n 1)*(2n 3)]}/4

[=中括,{=大括,/=除.*=乘,-=減

1/(1*3)-1/[(2n 1)*(2n 3)]}/4

是公式來的O

緊記!
參考: myself


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