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Ratio Test - Lim sup and lim inf version -

  1. Mar 19, 2010 #1
    Hello friends,

    1. The problem statement, all variables and given/known data
    [tex] lim sup |\frac{a_{n+1}}{a_{n}}|[/tex]

    I know that this operation tests for convergence, but I don't understand how it's related to [tex] lim_{n -> \infty}|\frac{a_{n+1}}{a_{n}}|[/tex]

    I understand that both will give the same result, but how is the latter different? lim sup is the sup of the collection of sub-sequential limits, so what does it mean when we take [tex] lim sup |\frac{a_{n+1}}{a_{n}}|[/tex] ?

    I appreciate your help,

  2. jcsd
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