maths induction
回答 (2)
2015-02-01 3:18 am
✔ 最佳答案
Please confirm:a(1) = 1
a(n) = [12 a(n - 1) + 12] / [a(n - 1) + 13]
Show that a(n) ≤ 3 for all positive integers n.
2015-01-31 19:18:09 補充：
Please read:
圖片參考：https://s.yimg.com/rk/HA00430218/o/649233705.png
2015-02-01 03:20:00 補充：
Sure!
In any way, we are combining two facts:
(1) a(k) = [12 a(k-1) + 12] / [a(k-1) + 13]
(2) a(k) ≤ 3
2015-02-01 11:12 am
Assume a(k) = [12 a(k-1) + 12] / [a(k-1) + 13] ≤ 3
When n=k+1,
a(k+1) = [12 a(k) + 12] / [a(k) + 13]
a(k) = [13 a(k+1) - 12] / [ 12 - a(k+1) ] ≤ 3
13 a(k+1) - 12 ≤ 36 - 3 a(k+1)
a(k+1) ≤ 48/16 = 3
Can I do it like this?
2015-02-01 12:12:27 補充：
THX =)
When n=k+1,
a(k+1) = [12 a(k) + 12] / [a(k) + 13]
a(k) = [13 a(k+1) - 12] / [ 12 - a(k+1) ] ≤ 3
13 a(k+1) - 12 ≤ 36 - 3 a(k+1)
a(k+1) ≤ 48/16 = 3
Can I do it like this?
2015-02-01 12:12:27 補充：
THX =)
收錄日期: 2021-04-15 18:07:25
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150131000051KK00069