I encountered the following serie during an optimization problem:
$\sum_{i=1}^N \frac{a_i + b_i \log(c_i - x)}{c_i - x}$
I need to find the roots of that serie, but I cannot find the way to find a closed-form expression for x. I don't even know if it is possible. What method would you use to approach this problem?
Thank you very much!