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Power series convergence

  1. May 19, 2013 #1
    1. The problem statement, all variables and given/known data
    Let Ʃanx^n and Ʃbnx^n be two power series and let A and B be their converging radii. define dn=max(lanl,lcnl) and consider the series Ʃdnx^n. Show that the convergence radius of this series D, is D=min(A,B)


    2. Relevant equations
    My idea is to use that the series Ʃ(lanl+lbnl)x^n has convergence radius min(A,B) and use that lanl+lbnl≥dn. Do you agree that this is a good idea from a rigorous perspective? Last assigment I really got punished for not being rigorous enough, so I want to make sure this time, that I do it properly.


    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. May 19, 2013 #2

    LCKurtz

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    That will show the radius of convergence of ##\sum d_n## is at least min(A,B). You would still have to show it isn't greater than that.
     
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