Limit question

  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. arildno

    arildno 12,015
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    "Do not opine, PROVE!"



    Apocryphal quote from Euclid. :smile:
     
  4. CRGreathouse

    CRGreathouse 3,682
    Science Advisor
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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.
     
  5. i have dealt with sup but not with inf but i will look them up. Thx anyway.
     
  6. manooch



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

    Accordingly this sequence isn't convergent:smile:
     
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