 Solution

At $x_n=0$ and $y_n=hn$, every radial pair displacement vanishes, so $f_x^n=0$. The particles with indices $n+l$ and $n-l$ give opposite azimuthal accelerations,which cancel pairwise. The acceleration sum has absolute convergence because ${\sum }_{l\ge 1}{l}^{-2}<\infty$. With zero velocities and $x_n=0$, both the Coriolis force and radial tidal force vanish. The equally spaced row is therefore an equilibrium of the infinite gravitating particle lattice. Its absolute gravitational potential would require an additional reference or regularization; the acceleration used here is well defined.