What function does $\sum \limits_{n=1}^{\infty}\frac{1}{n3^n}$ represent, evaluated at some number $x$? I need to know what the function $$\sum \limits_{n=1}^{\infty}\frac{1}{n3^n}$$ represents evaluated at a particular point.

For example if the series given was $$\sum \limits_{n=0}^{\infty}\frac{3^n}{n!}$$ the answer would be $e^x$ evaluated at $3$.

Yes, this is homework, but I'm not looking for any handouts, any help would be greatly appreciated.
Let $f(x)=\sum_1^{\infty}{1\over nx^n}$; you've got $f(3)$, so you want to know what $f(x)$ is. Differentiate it.
We have $ \displaystyle -\ln(1-x) = \sum_{n \geq 1 } \frac{x^n}{n} $ by course for $|x|&lt;1$ 
So this is simply $f(x)=-ln(1-x) $ evaluated at $x=\frac{1}{3}$
 Which gives the value :  $-\ln(1-\frac{1}{3})=\ln(\frac{3}{2})$