After fixing up my algebra, I ended up with the equation
$$\begin{aligned}
U_2-U_1 &= 0 \\
&= L\frac{N-1}{2}\sum_{j=1}^{N-2}{\csc\left(\frac{j\pi}{N-1}\right)}
+ L(N-1)2
- L\frac{N}{2}\sum_{j=1}^{N-1}{\csc\left(\frac{j\pi}{N}\right)} \\
&=...
Chapter 24, Question 61
Given two configurations, ##C_1##, ##C_2## of ##N## point charges each, determine the smallest value of ##N## s.t. ##V_1>V_2##.
##C_1##:
##N## point charges are uniformly distributed on a ring s.t. the distance between adjacent electrons is constant
##C_2##:
##N-1##...