作者Honor1984 (希望願望成真)
看板trans_math
標題Re: [極限]
時間Mon Sep 29 13:24:31 2008
※ 引述《Honor1984 (希望願望成真)》之銘言：
※ 引述《Qmmm (Q蛆蛆)》之銘言：
: 設a_1+ a_2+ ....+ a_n= 3n^2
: 求 lim [ √(a_2+ a_4+ ...+ a_(2n))- √(a_1+ a_3+ a_5+ ...+ a_(2n-1))]= ?
: n→∞
(省略)
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※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 122.124.101.106
1F：→ Qmmm:謝謝~ 202.151.60.129 09/29 11:19
2F：推 andy2007:請問 a_1 + ... + a_2n = 12n^2 = A + B140.125.205.230 09/29 11:58
a_1+ a_2+ ....+ a_n = f(n) = 3n^2
n -> 2n
3n^2 -> 3*4n^2
3F：→ andy2007:和 a_n = 3[(n)^2 - (n-1)^2] = 3(2n-1)140.125.205.230 09/29 11:58
n n-1
a_n = Σa_k - Σa_k
4F：→ andy2007:這兩行是怎麼來的呢 ? 程度差 煩請指導140.125.205.230 09/29 11:59
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※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 122.124.105.166
5F：推 andy2007:原來如此 還有一個問題140.125.205.230 09/29 14:09
6F：→ andy2007:A = Σ3[2*2k-1] = 6(n+1)n - 3n140.125.205.230 09/29 14:09
7F：→ andy2007:那個是算偶數項的總和嗎?那個2K是...140.125.205.230 09/29 14:10
8F：→ andy2007:最後n是怎麼來的? ...麻煩了Orz...140.125.205.230 09/29 14:11
9F：→ Honor1984:是算偶數項總和沒錯 但我用2k表示,k為連122.124.105.166 09/29 14:34
10F：→ Honor1984:續整數 只是計算方法的問題122.124.105.166 09/29 14:34
11F：推 andy2007:是3(2n-1) n用2k代入嗎 我糊塗了140.125.205.230 09/29 15:11
12F：推 andy2007:逆推 3n[2(n+1)-1] 好像怪怪的140.125.205.230 09/29 15:26
13F：推 changefly:A = Σ3[2*2k-1] = 6(n+1)n - 3n 59.124.112.124 09/29 15:29
14F：→ changefly:請問這段是如何整理出來的呢? 59.124.112.124 09/29 15:29