(adsbygoogle = window.adsbygoogle || []).push({}); Understanding series?????

The question in the book states Find the values of x for which the series converges, Find the sum of the series for those valuese of x

this is the series [tex]\sum_{n=1}^{\infty}\frac{x^n}{3^n}[/tex]

first of all I dont even really understand what its saying, is it saying find the sum and set x equal to it.? The first thing I did was write out the first few terms [tex][\frac{x}{3}],[\frac{x^2}{9}],[\frac{x^3}{27}][/tex] so this thing is geometric and [tex]a=\frac{x}{3}[/tex] with the ratio [tex]r=\frac{x}{3}[/tex] am I assuming that that the ratio is less than one b/c if not you cant even go anyfurther can you? well anyway after that by using the [tex]\frac{a}{1-r}[/tex] theorm I get [tex]\frac{x}{3-x}[/tex] where do I go from here? Im pretty confused If this was a series with real numerical values I would have been done with the question b/c I have already fournd the sum...but what next...should there be another function that I set this equal to to get the "values of x" that the book wants

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# Understanding series?

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