SCHWEITZER 1997 Problem 5

Let $a_1>a_2>a_3>\cdots$ be a sequence of real numbers which converges to 0. We put circles of radius $a_1$ into a unit square until no more can fit. (A previously laid circle must not be moved.) Then we put circles of radius $a_2$ in the remaining space until no more can fit, continuing the process for $a_3$ ,... What can the area covered by the circles be?

a similar problem involving circles in a square: https://artofproblemsolving.com/community/c7h1979044