版块导航: 正在加载中...

登录注册

应《网络安全法》要求，自2017年10月1日起，未进行实名认证将不得使用互联网跟帖服务。为保障您的帐号能够正常使用，请尽快对帐号进行手机号验证，感谢您的理解与支持！

24小时热门版块排行榜

北京石油化工学院2026年研究生招生接收调剂公告

返回列表

当前只显示满足指定条件的回帖，点击这里查看本话题的所有回帖

wc596520206

金虫 (正式写手)

应助: 2 (幼儿园)
金币: 1365.1
散金: 353
红花: 3
帖子: 486
在线: 78.8小时
虫号: 2416257
注册: 2013-04-13
专业: 运筹学

[求助] 大家看看给点思路也行，只要1和3.第一个看起来不难。

大家帮帮忙

619b62f9bc5c2406.jpg

回复此楼

» 猜你喜欢

求调剂，一志愿南京航空航天大学大学，080500材料科学与工程学硕已经有4人回复
考研调剂已经有9人回复
304材料求调剂已经有4人回复
一志愿郑大085600，310分求调剂已经有3人回复
317求调剂已经有7人回复
复试调剂，一志愿南农083200食品科学与工程已经有4人回复
一志愿太原理工安全工程300分，求调剂已经有3人回复
284求调剂已经有11人回复
食品工程专硕求调剂已经有3人回复
324求调剂已经有7人回复

» 本主题相关价值贴推荐，对您同样有帮助:

哪位大神来指导下数字信号处理怎么学，感激不尽已经有30人回复

1楼 2014-11-25 11:00:05

已阅回复此楼关注TA 给TA发消息送TA红花 TA的回帖

wc596520206

金虫 (正式写手)

应助: 2 (幼儿园)
金币: 1365.1
散金: 353
红花: 3
帖子: 486
在线: 78.8小时
虫号: 2416257
注册: 2013-04-13
专业: 运筹学

请大家再做一下第二题

赞一下

回复此楼

7楼2014-11-26 08:07:23

已阅回复此楼关注TA 给TA发消息送TA红花 TA的回帖

查看全部 8 个回答

wc596520206

金虫 (正式写手)

应助: 2 (幼儿园)
金币: 1365.1
散金: 353
红花: 3
帖子: 486
在线: 78.8小时
虫号: 2416257
注册: 2013-04-13
专业: 运筹学

应该都是关于数论的题目

赞一下

回复此楼

2楼2014-11-25 11:25:18

已阅回复此楼关注TA 给TA发消息送TA红花 TA的回帖

hank612

至尊木虫 (著名写手)

数学EPI: 14
应助: 225 (大学生)
金币: 14270.6
散金: 1055
红花: 95
帖子: 1526
在线: 1375.8小时
虫号: 2530333
注册: 2013-07-03
性别: GG
专业: 理论和计算化学

【答案】应助回帖

★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ...
感谢参与，应助指数 +1
wc596520206(feixiaolin代发): 金币+10 2014-11-25 20:18:22
wc596520206: 金币+50, ★★★★★最佳答案 2014-11-28 17:02:40

1. Clearly $\sum_{i=1}^{N}\frac{1}{i}\leq \prod_{p\leq N}\sum_{j=0}^{\left \lceil\log_p{N}\right \rceil}\frac{1}{p^j}$ , which is $\leq \prod_{p\leq N}\sum_{j=0}^{K}\frac{1}{p^j}=\prod_{p\leq N}\frac{1-\frac{1}{p^{K+1}}}{1-\frac{1}{p}}/latex]. <br /> <br /> Now as [latex]\lim_{x\rightarrow 0+}\frac{x}{-\ln(1-x)}=1$ , thus two positive series $\sum_{p }\frac{1}{p}$ and $\ln(\prod_{p}\frac{1}{1-\frac{1}{p}})$ are either both divergent or both convergent. But the latter is divergent according to the above inequality, so both series are divergent.

3.Step (i) Let us show that if a metric space (X, d) has at least two distinct cluster points (limit point) p and q, then it has a subset which is neither open nor closed.

Take a sequence {x_n} approaching to (in a metric space, “approaching” means $d(x_n,a) \rightarrow 0$ ) p, and a sequence {y_n} approaching to q. Without loss of generality, assume $\{x_n, p, q, y_n\}_{n=1}^{\infty}$ are all distinct points of X. Then let the set $A=\{x_{2n}, p, y_{2n}\}_{n=1}^{\infty}$ .

If A is open, then the point p has an open neibourhood in A, which is impossible as the sequence x_{2n+1} is not in A but approaches to p. If A is closed, then A^c (A complement) is an open set. This is still impossible as y_{2n} is not in A^c but approaches to q in A^c.

Step (ii). If the space only has at most one limit point, we discuss by cases.

Case 1. No limit point. Then every point has an open neibourhood which contains only itself. Thus every single point is an open set. Because any union of open set is still open, hence arbitary subset of X is open (therefore is closed too).

Case 2. The point x is the only limit point. Then every point other than x is an open set. This means that any set which excludes x is open. If a set A contains the point x, then since A^c is open so A is closed.

Combining steps (i) and (ii), we prove the claim.

赞一下

回复此楼

We_must_know. We_will_know.

3楼2014-11-25 14:13:46

已阅回复此楼关注TA 给TA发消息送TA红花 TA的回帖

hank612

至尊木虫 (著名写手)

数学EPI: 14
应助: 225 (大学生)
金币: 14270.6
散金: 1055
红花: 95
帖子: 1526
在线: 1375.8小时
虫号: 2530333
注册: 2013-07-03
性别: GG
专业: 理论和计算化学

引用回帖:

3楼: Originally posted by hank612 at 2014-11-25 14:13:46
1. Clearly \sum_{i=1}^{N}\frac{1}{i}\leq \prod_{p\leq N}\sum_{j=0}^{\left \lceil\log_p{N}\right \rceil}\frac{1}{p^j}, which is \leq \prod_{p\leq N}\sum_{j=0}^{K}\frac{1}{p^j}=\prod_{p\leq N}\frac{1- ...

the first part misses a [, then everything looks weird. I re-post it.

1.Clearly $\sum_{i=1}^{N}\frac{1}{i}\leq \prod_{p\leq N}\sum_{j=0}^{\left \lceil\log_p{N}\right \rceil}\frac{1}{p^j}$ , which is $\leq \prod_{p\leq N}\sum_{j=0}^{K}\frac{1}{p^j}=\prod_{p\leq N}\frac{1-\frac{1}{p^{K+1}}}{1-\frac{1}{p}}$ .

Now as $\lim_{x\rightarrow 0+}\frac{x}{-\ln(1-x)}=1$ , thus two positive series $\sum_{p}\frac{1}{p}$ and $\ln(\prod_{p}\frac{1}{1-\frac{1}{p}})$ are either both divergent or both convergent. But the latter is divergent according to the above inequality, so both series are divergent.

赞一下

回复此楼

We_must_know. We_will_know.

4楼2014-11-25 14:19:00

已阅回复此楼关注TA 给TA发消息送TA红花 TA的回帖

查看全部 8 个回答

最具人气热帖推荐 [查看全部]		作者	回/看	最后发表

[考研] 294分080500材料科学与工程求调剂 +4	柳溪边 2026-03-26	4/200	2026-03-26 21:14 by XPU李庆
[考研] 291求调剂 +9	hhhhxn.. 2026-03-23	9/450	2026-03-26 18:59 by 不吃魚的貓
[考研] 中国科学院深圳先进技术研究院-光纤传感课题组招生-中国科学院大学、深圳理工大学联培 +5	YangTyu1 2026-03-26	5/250	2026-03-26 18:27 by 猫咪猫咪呀
[考研] 352求调剂 +4	大米饭！ 2026-03-22	4/200	2026-03-26 16:40 by 不吃魚的貓
[考研] 334分一志愿武理材料求调剂 +4	李李不服输 2026-03-26	4/200	2026-03-26 16:00 by 不吃魚的貓
[考研] 0856调剂 +4	求求让我有书读� 2026-03-26	5/250	2026-03-26 15:54 by dick_runner
[考研] 一志愿北京化工大学材料与化工 264分各科过A区国家线 +6	哈哈157349 2026-03-21	6/300	2026-03-26 10:39 by 醉在风里
[考研] 085600 材料与化工 329分求调剂 +9	Mr. Z 2026-03-25	9/450	2026-03-26 10:36 by baoball
[考研] 一志愿哈工大，085400，320，求调剂 +4	gdlf9999 2026-03-24	4/200	2026-03-25 23:01 by boxking200
[考研] 07化学303求调剂 +5	睿08 2026-03-25	5/250	2026-03-25 22:46 by 418490947
[考研] 考研调剂 +6	来好运来来来 2026-03-21	7/350	2026-03-25 22:43 by 418490947
[考研] 求调剂 +3	李李不服输 2026-03-25	3/150	2026-03-25 13:03 by cmz0325
[考研] 340求调剂 +5	话梅糖111 2026-03-24	5/250	2026-03-25 06:53 by ilovexiaobin
[考研] 生物学学硕求调剂 +7	小羊睡着了? 2026-03-23	10/500	2026-03-25 02:24 by 清风拂扬。 m
[考研] 276求调剂。有半年电池和半年高分子实习经历 +9	材料学257求调剂 2026-03-23	10/500	2026-03-24 07:36 by wangy0907
[论文投稿] 急发核心期刊论文 +3	贤达问津 2026-03-23	5/250	2026-03-23 17:13 by 妹子不好惹
[考研] 276求调剂 +3	YNRYG 2026-03-21	4/200	2026-03-23 08:31 by 醉在风里
[考研] 280分求调剂一志愿085802 +4	PUMPT 2026-03-22	7/350	2026-03-22 22:13 by 星空星月
[考研] 285求调剂 +6	ytter 2026-03-22	6/300	2026-03-22 12:09 by 星空星月
[考研] 一志愿南理工085701环境302求调剂院校 +3	葵梓卫队 2026-03-20	3/150	2026-03-20 19:28 by zhukairuo

24小时热门版块排行榜

wc596520206

[求助] 大家看看 给点思路也行，只要1和3.第一个看起来不难。

» 猜你喜欢

» 本主题相关价值贴推荐，对您同样有帮助:

wc596520206

wc596520206

hank612

【答案】应助回帖

hank612

[求助] 大家看看给点思路也行，只要1和3.第一个看起来不难。