This was part of an answer posted as a solution to the problem. Of course after differentiating you would need to integrate to get back to $f(x)$ but this part has been left out as it's the differentiation part I am stuck on. 

Question: Find the power series representation for the function and determine the radius of convergence. 

$f(x) = $ln$(5-x)$

$$f'(x) = -\frac{1}{5-x}$$

$$= - \frac{1}{5}\cdot \frac{1}{1-1/5x}$$

$$= - \frac{1}{5} \sum\_{n=0}^{\infty}(\frac{1}{5}x)^n$$

$$= -\sum\_{n=0}^{\infty}\frac{x^n}{5^{n+1}}$$ 

The last step is where I am confused. In the denominator where are they getting the $n+1$ from?