Students need to learn to understand the physical and geometric meaning of ${1}\over {|\Vec r - \Vec r'|}$.
This activity can be thought of as a warm-up for a series of activities that focus on unpacking successively more complicated superposition integrals.
Although students typically have some experience with power series from math courses, this activity allows them to employ the common physics strategy of substituting into known series by rewriting an expression in terms of dimensionless parameters. (same link as “expand this potential”)