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Prove sequences

  1. Dec 24, 2011 #1
    1. The problem statement, all variables and given/known data
    prove that if k>1 then kn→∞ an n→∞

    there is a hint given. (hint:let k=1+t where t>0 and use the fact that (1+t)n>1+nt)

    (ii) prove that if 0<k<1 then kn→0 as n→∞
    2. Relevant equations



    3. The attempt at a solution
    if k>1
    then kn+1-kn=kn(k-1)

    (ii) 1/k>1
    then1/kn→∞
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 24, 2011 #2

    SammyS

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    This appears to have a typo in it. It should read:
    kn+1-kn=kn(k-1)​
    For (i), try using the hint.

    Should you be using an ε - δ argument for this ?
     
  4. Dec 24, 2011 #3
    the hint doesnt make sense to me and i think it is ussing epsilon-delta
     
  5. Dec 24, 2011 #4

    SammyS

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    Excuse me,

    I believe that I should have said ε - N.

    DUH !!!
     
  6. Dec 24, 2011 #5
    yh ur right, but how would i aproach this
     
  7. Dec 24, 2011 #6
    Help!!!!!!!!!!
     
  8. Dec 24, 2011 #7

    SammyS

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    Pretty much what you need to show is that given any number, M > 0, (no matter how large) there exists a natural number, N, such kn > M, for all n > N .

    I presume you have some similar criterion for showing that limn→∞an[/SUB= ∞ .
     
  9. Dec 24, 2011 #8

    Ray Vickson

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    What is it about the hint that is confusing you? Using the hing is by far the easiest way of doing (i). And, if you don't want to use an unsubstantiated hint, proving it is easy enough, just by induction (assuming t > 0, of course).

    RGV
     
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