mateforum.ro Forum Index mateforum.ro

 
 FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

Divergenta sirului armonic H_{n}=1+1/2+...+1/n

 
Post new topic   Reply to topic    mateforum.ro Forum Index -> Clasa a XI-a -> Intrebari teoretice
View previous topic :: View next topic  
Author Message
Cezar Lupu
Site Admin


Joined: 26 Sep 2007
Posts: 629
Location: Pittsburgh/Craiova/Bucharest/Constanta

PostPosted: Sat Sep 29, 2007 12:51 pm    Post subject: Divergenta sirului armonic H_{n}=1+1/2+...+1/n Reply with quote

Sa se arate ca sirul armonic H_{n}=1+\frac{1}{2}+\dots +\frac{1}{n} este divergent.
_________________
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
Back to top
View user's profile Send private message Visit poster's website Yahoo Messenger
Laurentiu Tucaa
Thales


Joined: 22 Mar 2009
Posts: 148
Location: Pitesti sau Bucuresti

PostPosted: Mon Apr 06, 2009 7:37 pm    Post subject: Reply with quote

Pai nu e sir Cauchy, deci este divergent.
Demostratia este simpla: |x_{2n}-x_n|=\frac {1}{n+1}+\frac {1}{n+2}+...+\frac {1}{2n}>n\frac{1}{2n}=\frac{1}{2}. In concluzie (H_n) nu este sir Cauchy, deci este divergent.
Back to top
View user's profile Send private message
cipriancx
Euclid


Joined: 16 Nov 2008
Posts: 34
Location: Bucuresti,Bacau

PostPosted: Fri Jun 12, 2009 1:45 pm    Post subject: Reply with quote

H_{n}=1+\frac{1}{2}+\dots +\frac{1}{n}-\ln n=c, unde c este o constanta (constanta lui Euler parca).
Asadar H_{n}=c+ln n iar c+\ln n tinde la infinit, rezulta ca sirul (H_{n}) este divergent.
Back to top
View user's profile Send private message Visit poster's website
Display posts from previous:   
Post new topic   Reply to topic    mateforum.ro Forum Index -> Clasa a XI-a -> Intrebari teoretice All times are GMT + 2 Hours
Page 1 of 1

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum



Powered by phpBB © 2001, 2005 phpBB Group