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Limsupremum calculation horrible difficulty

  1. Oct 23, 2010 #1
    1. The problem statement, all variables and given/known data
    Calculate the radius of convergence of [itex]\sum_{n=0}^\infty a_{n}z^{2n}[/itex]
    let [itex]\sum_{n=0}^\infty a_{n}z^{n}[/itex]with radius R

    2. Relevant equations
    [itex]\limsup|a_n|^{\frac{1}{n}}=\limsup |\frac{a_{n+1}}{a_n}|[/itex]


    3. The attempt at a solution
    [tex]\limsup|a_n|^{\frac{1}{n}}=\lim_{k\to\infty}|a_{2k}|^{\frac{1}{2k}}[/tex]
    then how to write the "ratio".............
    the latex is killin me please help.............
     
    Last edited: Oct 23, 2010
  2. jcsd
  3. Oct 24, 2010 #2
    You could use the limsup formula, but it's easier to think about what the radius of convergence means. Basically you're given that the original series converges for |z| < R and diverges for |z| > R, so what happens when you square z?
     
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