The ratio of wavelength values of series limit lines (n₂ = ∞ ) of Balmer series and Paschen serie are

Balmer series n₁ = 2, $\overline{\mathrm{v}}=\frac{1}{\mathrm{\lambda }}={\mathrm{R}}_{\mathrm{H}}\left(\frac{1}{2^2}-\frac{1}{{\infty }^2}\right)$

Series limit$=\frac{{\mathrm{R}}_{\mathrm{H}}}{4}$

Series limit λ = 4/R_H 

Paschen series, n₁ = 3

$\overline{\mathrm{v}}=\frac{1}{\mathrm{\lambda }}={\mathrm{R}}_{\mathrm{H}}\left(\frac{1}{3^2}-\frac{1}{{\infty }^2}\right)$

Series limit $=\frac{{\mathrm{R}}_{\mathrm{H}}}{9}$

Series limit

λ = 9/R_H

The ratio of wavelength values of series limit lines (n₂ = ∞ ) of Balmer series and Paschen serie are = 4 : 9