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Homework Help: Find the radius of convergence

  1. Dec 14, 2008 #1
    The problem statement, all variables and given/known data
    Find the radius of convergence of the Series:
    [tex]\sum_{i=1}^{\infty}\frac{(2n)!x^n}{(n!)^2}[/tex]

    The attempt at a solution
    I used the Ratio Test but I always get L = [tex]|\frac{2x}{n+1}|[/tex]

    The answer is 1/4. I think im mistaking with factorial.
     
  2. jcsd
  3. Dec 14, 2008 #2
    Solved. The problem was tha
    (2(n+1))! = (2n + 2)(2n + 1)(2n)!
    and I was doing (2(n+1))! = (2n + 2)(2n)!
    because i thought you should distribute the 2
     
  4. Dec 14, 2008 #3
    Ah it is always good to find your own mistake. Off the bat that was my guess... Sadly I got in the thread too late.
     
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