1. Limited time only! Sign up for a free 30min personal 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!

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

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

Have something to add?
Draft saved Draft deleted