Wavelength can be given by
where n is upper energy level and n' is lower energy level.
Energy in photon is inversely proportional to wavelength & directly proportional to frequency.
( E = h v = h c / lambda = k R [ 1/n' ^2 - 1/n^2 ]
Paschen series are transitions down to level n=3. Longest wavelength corresponds to lowest photon energy, is for n=4 to n=3. Shortest wavelength (highest photon energy) is for n = infinity (free electron) to n=3.
Highest photon energy, Eh = k (1/3² - 1/infinity²) = k (1/3² - 0) = 0.111 k
Lowest photon energy, El = k (1/3² - 1/4²) = 0.0486 k
λshort = Shortest wavelength: 3² / R = 9 /R
λlong = Longest wavelength : 1/ (0.0486 R) = 20.57 / R
If you want the ratio of longest to the shortest wavelengths:
λlong / λshort = Eh / El = 2.29