Series (finding the interval of convergence)

[DivGradCurl]

\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}

\textrm{How can I obtain the interval of convergence of the given series? Thanks.} :smile:

[DivGradCurl]

\textrm{I forgot to say\ldots How do I find it without the need to apply the \textit{ratio test}? Thank you. }