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Homework Help: Real Analysis Question regarding Series

  1. Feb 26, 2008 #1
    1. The problem statement, all variables and given/known data

    Let {a_n} be a monotonically decreasing sequence of positive real numbers with lim a_n = 0. Show the radius of convergence of [tex]\sum[/tex]a_nx[tex]^{}n[/tex] is at least 1.

    3. The attempt at a solution
    I have no real attempt at a solution since I'm unsure how to proceed. I've tried using the power series definition and using a fixed x_0, but I get nowhere using this method. Can someone outline how this proof might look? Thanks.
  2. jcsd
  3. Feb 26, 2008 #2


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    The radius of convergence is given by
    [tex]\lim_{n \to \infty} \left| \frac{a_n}{a_{n+1}} \right|.[/tex]

    If {a_n} is decreasing and lim a_n = 0, then what can we say about this limit?
  4. Feb 26, 2008 #3
    Is the fact that [itex]a_n = 0[/itex] as n approaches infinity needed? I find no reason for it.
  5. Feb 26, 2008 #4
    Solved It!

    Solved It!
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