[Krystalsnow2013]

Using this link: https://pdf.ac/H0G5w

How can we use the equation and the given values to find the N initial and N final, as well as being confused about how those two are correlated with the analysis? But with the shared values, how do we find those initial and final values, and how would we go about answering those questions?

[Borek]

Trial and error mostly.

Probably the fastest brute force way is to build a spreadsheet that will calculate energies/wavelengths for every combination of n₁ and n² between - say - 1 and 7 (mostly copy and paste, so quite quick), and look for values from the table.

[Corribus]

You could also just look up which hydrogen spectral series have lines in the visible and that should give you a good clue of what the lower lying state is.