Physics Forums

Physics Forums (http://www.physicsforums.com/index.php)
-   Calculus (http://www.physicsforums.com/forumdisplay.php?f=109)
-   -   Limit question (http://www.physicsforums.com/showthread.php?t=133664)

vabamyyr Sep26-06 10:47 AM

limit question
 
I have a question:

what is lim (n--->infinity)= 1/(3+(-1)^n))? My opinion that this limit does not exist.

arildno Sep26-06 10:50 AM

"Do not opine, PROVE!"



Apocryphal quote from Euclid. :smile:

CRGreathouse Sep26-06 11:44 AM

Are you asking about
[tex]\lim_{n\rightarrow\infty}\frac{1}{3+(-1)^n}[/tex]
perhaps? The equals sign in your post is confusing me. If so, are you familiar with the lim sup and lim inf? That would give you an easy direct proof: if lim sup = lim inf, that's the limit; otherwise, the limit does not exist.

vabamyyr Sep26-06 01:20 PM

i have dealt with sup but not with inf but i will look them up. Thx anyway.

manoochehr Oct1-06 09:12 PM

manooch
 
Quote:

Quote by vabamyyr
I have a question:

what is lim (n--->infinity)= 1/(3+(-1)^n))? My opinion that this limit does not exist.



if n∈Z (Z=Integer) then we have two answer for equation

1) if n=Even then answer=1/4

2) if n=Odd then answer=1/2

if n∈R (R=Real) then equation is undefined

for example: (-1)^1/2 does not exist.:smile:

d_leet Oct1-06 09:16 PM

Quote:

Quote by manoochehr

for example: (-1)^1/2 does not exist.:smile:

It certainly does, it just isn't real.

Edgardo Oct2-06 04:45 PM

I think you could use:

Proposition 4 Every subsequence of a convergent sequence converges to the same limit.
from: http://www.iwu.edu/~lstout/sequences/node3.html

manoochehr Oct2-06 08:48 PM

thank you for help me

manoochehr Oct3-06 05:36 AM

thank you for conduce:tongue:

Accordingly this sequence isn't convergent:smile:


All times are GMT -5. The time now is 07:32 PM.

Powered by vBulletin Copyright ©2000 - 2014, Jelsoft Enterprises Ltd.
© 2014 Physics Forums