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 vabamyyr Sep26-06 11:47 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 11:50 AM

"Do not opine, PROVE!"

Apocryphal quote from Euclid. :smile:

 CRGreathouse Sep26-06 12:44 PM

$$\lim_{n\rightarrow\infty}\frac{1}{3+(-1)^n}$$
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 02:20 PM

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

 manoochehr Oct1-06 10:12 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

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

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

 d_leet Oct1-06 10:16 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 05:45 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 09:48 PM

thank you for help me

 manoochehr Oct3-06 06:36 AM

thank you for conduce:tongue:

Accordingly this sequence isn't convergent:smile:

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