Re: [中學] 遞迴數列

看板Math作者LPH66 (IS YOU)時間4年前 (2019/06/20 22:08)推噓7(7推 0噓 7→)

留言14則, 6人參與討論串11/11 (看更多)

※ 引述《banmi (數學小天兵)》之銘言： : a_{n+1}=2a_{n}(1-a_{n}),且 a_{0}=2,n=0,1,2,3,... : 求 a_{n} 的一般式。 : 小弟土法鍊鋼鍊了一下,找不太到規律,希望有大大可以幫忙解惑。配方得 a_{n+1} = -2(a_n - 1/2)^2 + 1/2 移項後可變成 a_{n+1} - 1/2 = -2(a_n - 1/2)^2 把 -2 的負號也移到左邊: 1/2 - a_{n+1} = 2(1/2 - a_n)^2 所以就有推文這個代換: : → ZO20 : b_n=1/2-a_n 06/20 06:05 代換後變成 b_{n+1} = 2(b_n)^2 兩邊乘以 2 寫成 2 b_{n+1} = (2 b_n)^2, 再代換 c_n = 2 b_n 就成了 c_{n+1} = (c_n)^2, 這東西的通式容易得到是 c_n = (c_0)^(2^n) (平方平方一直疊上去) 首項是 b_0 = 1/2 - 2 = -3/2, c_0 = -3 所以 c_n = (-3)^(2^n), b_n = (-3)^(2^n)/2, a_n = [1 - (-3)^(2^n)]/2 -- 'You've sort of made up for it tonight,' said Harry. 'Getting the sword. Finishing the Horcrux. Saving my life.' 'That makes me sound a lot cooler then I was,' Ron mumbled. 'Stuff like that always sounds cooler then it really was,' said Harry. 'I've been trying to tell you that for years.' -- Harry Potter and the Deathly Hollows, P.308 -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 180.177.3.123 (臺灣) ※ 文章網址: https://www.ptt.cc/bbs/Math/M.1561039727.A.865.html

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alan23273850

06/21 12:19, 4年前 , 1^F

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chemmachine

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chemmachine

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