作者Honor1984 (希望愿望成真)
看板trans_math
标题Re: [极限]
时间Mon Sep 29 13:24:31 2008
※ 引述《Honor1984 (希望愿望成真)》之铭言：
※ 引述《Qmmm (Q蛆蛆)》之铭言：
: 设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)
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 122.124.101.106
1F：→ Qmmm:谢谢~ 202.151.60.129 09/29 11:19
2F：推 andy2007:请问 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:这两行是怎麽来的呢 ? 程度差 烦请指导140.125.205.230 09/29 11:59
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 122.124.105.166
5F：推 andy2007:原来如此 还有一个问题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:那个是算偶数项的总和吗?那个2K是...140.125.205.230 09/29 14:10
8F：→ andy2007:最後n是怎麽来的? ...麻烦了Orz...140.125.205.230 09/29 14:11
9F：→ Honor1984:是算偶数项总和没错 但我用2k表示,k为连122.124.105.166 09/29 14:34
10F：→ Honor1984:续整数 只是计算方法的问题122.124.105.166 09/29 14:34
11F：推 andy2007:是3(2n-1) n用2k代入吗 我糊涂了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:请问这段是如何整理出来的呢? 59.124.112.124 09/29 15:29