okay im supposed to find a recurrence relation for
$$ a_{n+1}= b \cdot a_n + c \cdot n \ \ \ \ \ \ \ \ \ \ \ \ \mathbf{(1)} $$
where $b$ and $c$ are constants. the method we learned in class was to multiply each term by $x^n$ and then take the sum of of the equation which has always worked fine but the "$c \cdot n$" term is giving me trouble in this problem. after some manipulation i get $c \sum n \cdot x^n$ which obviously does not converge. i know $x^n$ converges to $1 \over{1-x}$ but i dont know what to do about the "$n$" term. any help would be appreciated.