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Series (finding the interval of convergence)

  1. Oct 2, 2004 #1
    [tex] \sum _{n=1} ^{\infty} \frac{x^n}{3^n} = \sum _{n=1} ^{\infty} \frac{x}{3} \left( \frac{x}{3} \right)^{n-1} = \frac{\frac{x}{3}}{1-\frac{x}{3}} = \frac{x}{3-x} [/tex]

    [tex] \textrm{How can I obtain the interval of convergence of the given series? Thanks.} [/tex] :smile:
  2. jcsd
  3. Oct 2, 2004 #2
    [tex] \textrm{I forgot to say\ldots How do I find it without the need to apply the \textit{ratio test}? Thank you. } [/tex]
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