1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Real Analysis Question regarding Series
  1. Real Analysis, Series (Replies: 3)

Loading...