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Sequence limits

  1. Dec 8, 2009 #1
    1. The problem statement, all variables and given/known data

    prove that lim(n[tex]\rightarrow\infty[/tex])(r1/n) = 1 for r> 0

    3. The attempt at a solution

    let [tex]\epsilon[/tex] > 0 be given we need to find n0 [tex]\in[/tex] N such that

    [tex]\left|[/tex]r1/n - 1 [tex]\left|[/tex] < [tex]\epsilon[/tex]

    but not really sure where to go from here?
     
  2. jcsd
  3. Dec 8, 2009 #2
    What if the problem was a little simpler -- proving that the limit as n approaches 0 of r^n equals 1. How would you go about doing that?
     
  4. Dec 9, 2009 #3
    1 < L [tex]\leq[/tex] r1/n

    implies

    1[tex]\leq[/tex] Ln [tex]\leq[/tex] r

    i'm not sure how this follows?
     
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