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Interval of convergence with binomial coefficient

  1. Jul 15, 2007 #1
    1. The problem statement, all variables and given/known data

    Find the radius of converge of:

    [tex]\sum[/tex]x[tex]^{}(n choose k)[/tex]

    2. Relevant equations

    Radius of converge = 1/limsup|an+1/an|, for power series: anx^n

    3. The attempt at a solution

    Tried rewriting (n choose k) as: n!/[k!(n-k)!]

    but where do I go from here? How do I take out x^n?
  2. jcsd
  3. Jul 15, 2007 #2
    How is the series defined?
    Is it,
    [tex]\sum_{n=k}^{\infty} x^{{n\choose k}}[/tex]

    For example,
    [tex]\sum_{n=0}^{\infty} x^{n!}[/tex]
    Use the ratio test.
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