Convert sum to function

Question

I need to convert $\sum_{i=0}^N \frac{C_1}{C_2+C_3i}$, to a function

$C_1$, $C_2$ and $C_3$ are constants.

I am interested in resulting function itself and method as well.

Answer 1

There is an answer to your question but the answer is extremely complex since $$\displaystyle f(N)=\sum_{k=0}^N \frac{C1}{C2+k C3}=\frac{\text{C1} \left(\psi ^{(0)}\left(\frac{\text{C2}}{\text{C3}}+n+1\right)-\psi ^{(0)}\left(\frac{\text{C2}}{\text{c3}}\right)\right)}{\text{C3}}$$ where appears the polygamma function