What we can deduce from hydrogen's line spectrum here is that at higher energy levels (i.e shorter wavelengths and higher frequencies, at the ultraviolet end of the spectrum) energy levels start to converge as the visible lines nearer to ultra violet become closer as higher energy levels come together. At a certain point, the electron's energy can no longer be quantized,this is the limit of convergence at which point the atom becomes ionized. Only the lines from the Balmer series lie within our visible spectrum, while Lyman's lies in the UV spectrum and Paschen's lies within the Infrared spectrum.