You’ve been working with some physicists who need to study, as part of their experimental design, the interactions among large numbers of very small charged particles. Basically, their setup works as follows. They have an inert lattice structure, and they use this for placing charged particles at regular spacing along a straight line. Thus we can model their structure as consisting of the points {1, 2, 3, . . . , n} on the real line; and at each of these points j, they have a particle with charge qj. (Each charge can be either positive or negative.) They want to study the total force on each particle, by measuring it and then comparing it to a computational prediction. This computational part is where they need your help. The total net force on particle j, by Coulomb’s Law, is equal to