1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

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