= 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,
$$
\frac{Gm}{h^2}\frac{l}{|l|^3}\mathbf e_y,\qquad -\frac{Gm}{h^2}\frac{l}{|l|^3}\mathbf e_y,
$$
which cancel pairwise. The acceleration sum has <absolute convergence> because $\sum_{l\ge1}l^{-2}<\infty$. With zero velocities and $x_n=0$, both the <Coriolis force> and radial <tidal force> vanish. \b[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.
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