Sequence M.I.
2011-09-15 5:38 am
圖片參考：http://i707.photobucket.com/albums/ww74/stevieg90/ScreenHunter_05Sep101524.gif
Show (a_n)^2>=2 by M.I. Only, no need to show it is decreasing, THX!
回答 (2)
2011-09-16 7:00 am
✔ 最佳答案
First, we can use induction to show that a_n > 0.Then, we can use AM-GM inequality
So, a_n = a_(n-1)/2 + 1/a_(n-1) ≧ 2*(1/2)^(1/2) = 2^(1/2)
Hence, (a_n)^2 ≧ 2
參考: myself
2011-09-15 6:20 am
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110914000015KK07156