作者EggAche (蛋疼)
看板trans_math
标题[极限] 99中正
时间Tue Apr 2 23:21:49 2013
1 + 2^(1/2) + 3^(1/3) + ... + n^(1/n)
求 lim ---------------------------------------
n->∞ n
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 36.234.220.137
1F：推 gj942l41l4:n*1/n<___<n*n^(1/n)/n 夹挤 58.115.232.119 04/02 23:42
2F：→ yhliu:令 a_n = n^{1/n}, 则 a_n→1 114.41.104.41 04/06 13:58
3F：→ yhliu:原式=lim(a_1+...+a_n)/n = 1. 114.41.104.41 04/06 13:58
4F：推 Sumino:夹挤会失败 n->∞ 2^1/2 < n^1/n? 不对吧.. 1.172.93.116 04/08 15:47
5F：→ suhorng:@4F: 夹挤是 1 < ... < n^(1/n) 118.166.52.167 04/08 20:27
6F：→ Sumino:什麽意思? 听不太懂楼上说的@@ 1.172.93.116 04/08 21:04
7F：→ Sumino:这题就是夹挤我凑不出来才想到用stolz 1.172.93.116 04/08 21:07
8F：推 suhorng:我想错了.. 118.166.52.167 04/08 21:10
9F：→ suhorng:抱歉 118.166.52.167 04/08 21:10
10F：→ Sumino:不会阿 XD 1.172.93.116 04/08 21:12
11F：推 gj942l41l4:想错了= =.. 140.112.217.22 04/09 00:19