> 
> Determinate the coefficient of $x^k $ of the generating function $f(x)=\frac{x}{1-3x}$
> 
> 
> 

Im trying to do this exercise but something seems wrong. If someone has hints I would appreciate. Thanks in advance
So, $f (x)=\frac{x}{1-3x}=- \frac{1}{3} \frac{1}{1- \frac{1}{3x}}=- \frac{1}{3} \sum ( \frac{1}{3x})^k$

So the coefficient is $-\frac{1}{3} ( \frac{1}{3})^k = - \frac{1}{3 \cdot 3^k} $