Limit question

  • Thread starter vabamyyr
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  • #1
vabamyyr
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I have a question:

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

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  • #2
arildno
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"Do not opine, PROVE!"



Apocryphal quote from Euclid. :smile:
 
  • #3
CRGreathouse
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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.
 
  • #4
vabamyyr
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i have dealt with sup but not with inf but i will look them up. Thx anyway.
 
  • #5
manoochehr
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manooch

vabamyyr said:
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:
 
  • #6
d_leet
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manoochehr said:
for example: (-1)^1/2 does not exist.:smile:

It certainly does, it just isn't real.
 
  • #7
Edgardo
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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
 
  • #8
manoochehr
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thank you for help me
 
  • #9
manoochehr
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thank you for conduce:tongue:

Accordingly this sequence isn't convergent:smile:
 

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