FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups 
 ProfileProfile   PreferencesPreferences   Log in to check your private messagesLog in to check your private messages   Log inLog in 
Forum index » Science and Technology » Math » Research
a limit problem
Post new topic   Reply to topic Page 1 of 1 [2 Posts] View previous topic :: View next topic
Author Message
zhangyi.zhangyi@gmail.com
science forum beginner


Joined: 10 Jul 2006
Posts: 1

PostPosted: Mon Jul 10, 2006 11:32 am    Post subject: a limit problem Reply with quote

Define that (n)_r=n(n-1)...(n-r+1),
what's the result of the limit:
lim_{n->\infty, r->\infty, r/n->p} (n-k)_r / (n)_r.

is it e^{-kp} ?
how to prove it?
Back to top
Einar Andreas Rødland
science forum beginner


Joined: 03 Jun 2005
Posts: 10

PostPosted: Mon Jul 10, 2006 4:09 pm    Post subject: Re: a limit problem Reply with quote

zhangyi.zhangyi@gmail.com wrote:
Quote:
Define that (n)_r=n(n-1)...(n-r+1),
what's the result of the limit:
lim_{n->\infty, r->\infty, r/n->p} (n-k)_r / (n)_r.

is it e^{-kp} ?
how to prove it?

First, using (n)_r = n!/(n-r)!, you see that
(n-k)_r / (n)_r = (n-r)_k / (n)_k.
Write this out, and you get
(n-r)/n * (n-r-1)/(n-1) * ... * (n-r-k+1)/(n-k+1).
The limit as n,r increases with r/n -> p is then
(1-p) * (1-p) * ... * (1-p) = (1-p)^k.

Einar
Back to top
Google

Back to top
Display posts from previous:   
Post new topic   Reply to topic Page 1 of 1 [2 Posts] View previous topic :: View next topic
The time now is Wed Jun 28, 2017 7:18 pm | All times are GMT
Forum index » Science and Technology » Math » Research
Jump to:  

Similar Topics
Topic Author Forum Replies Last Post
No new posts help on problem brb003 Math 0 Mon Aug 28, 2006 3:31 am
No new posts fraction problem mikerule Research 0 Thu Aug 24, 2006 5:10 am
No new posts Mod computer problem William Elliot Math 4 Fri Jul 21, 2006 12:07 pm
No new posts Divine apparitions in the tethered goat problem? jpalmour@gmail.com Math 6 Thu Jul 20, 2006 8:26 pm
No new posts possible to use Generalized Method of Moments for this pr... comtech Math 1 Thu Jul 20, 2006 12:49 am

Copyright © 2004-2005 DeniX Solutions SRL
Other DeniX Solutions sites: Electronics forum |  Medicine forum |  Unix/Linux blog |  Unix/Linux documentation |  Unix/Linux forums  |  send newsletters
 


Powered by phpBB © 2001, 2005 phpBB Group
[ Time: 0.0170s ][ Queries: 16 (0.0046s) ][ GZIP on - Debug on ]