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Limit question

  1. Sep 26, 2006 #1
    I have a question:

    what is lim (n--->infinity)= 1/(3+(-1)^n))? My opinion that this limit does not exist.
  2. jcsd
  3. Sep 26, 2006 #2


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    "Do not opine, PROVE!"

    Apocryphal quote from Euclid. :smile:
  4. Sep 26, 2006 #3


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    Are you asking about
    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.
  5. Sep 26, 2006 #4
    i have dealt with sup but not with inf but i will look them up. Thx anyway.
  6. Oct 1, 2006 #5

    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:
  7. Oct 1, 2006 #6
    It certainly does, it just isn't real.
  8. Oct 2, 2006 #7
  9. Oct 2, 2006 #8
    thank you for help me
  10. Oct 3, 2006 #9
    thank you for conduce:tongue:

    Accordingly this sequence isn't convergent:smile:
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