The reason why we only see the "Balmer Series" is because of its frequency(Energy of the photon = Planck's constant × frequency) corresponds to the visible light region in the electromagnetic spectrum.

What is visible light and why(+ how) is it visible to us humans?

All electromagnetic radiation is considered light, however only a percentage of electromagnetic radiation, which we refer to as visible light, is visible to humans. Our eyes' cone cells, which are a type of a photoreceptor cell in the retina, function as receivers that are calibrated to detect wavelengths in this particular region of the spectrum. There are wavelengths in other parts of the spectrum that are too intense(too big or small) for our biological senses to handle. (1)

The majority of humans can visually perceive wavelengths between around 400 nanometers (nm) and 780 nm. The limits of the visible spectrum for humans are not well defined; rather, they are spectrums themselves. Colour vision is the outcome of combining signals from three visual pigment types within cones: red, green, and blue, which correlate to cone types L, M, and S (RGB-LMS), respectively. This is also known as trichromatic color vision. These colours correspond to the wavelengths of peak light absorption intensities of the modified chromophores (a molecule which absorbs light at a particular wavelength and emits color as a result). Peak absorptions for L cones are found between 555 and 565 nm, M cones between 530 and 537 nm, and S cones between 415 and 430 nm. Therefore, colour vision results from the peak absorption levels of the shifted cones and, in the end, from the brain's interpretation of the makeup of these wavelength absorption points. The complete process is frequently referred to as the "retinoid cycle." (2) (As this is biology related, I won't dive deeper into it on Chem SE)

Interestingly, ageing processes in the eye cause changes in a person's vision and sensitivity to light during their lifetime. With ageing, the lens's transparency diminishes, particularly for the visible spectrum's short wavelength region (blue light). (3)

References:

(1) https://science.nasa.gov/ems/09_visiblelight/

 (2) https://www.ncbi.nlm.nih.gov/books/NBK470227/

 (3) https://www.bfs.de/EN/topics/opt/visible-light/introduction/introduction.html

The reason why we only see the "Balmer Series" is because of its frequency  (energy of the photon = Planck's constant × frequency) corresponds to the visible light region in the electromagnetic spectrum.

What is visible light and why  (and how) is it visible to us humans?

All electromagnetic radiation is considered light, however only a percentage of electromagnetic radiation, which we refer to as visible light, is visible to humans. Our eyes' cone cells, which are a type of a photoreceptor cell in the retina, function as receivers that are calibrated to detect wavelengths in this particular region of the spectrum. There are wavelengths in other parts of the spectrum that are too intense  (too big or small) for our biological senses to handle.⁽¹⁾

The majority of humans can visually perceive wavelengths between around 400 and 780 nanometers (nm). The limits of the visible spectrum for humans are not well defined; rather, they are spectrums themselves. Colour vision is the outcome of combining signals from three visual pigment types within cones: red, green, and blue, which correlate to cone types L, M, and S (RGB-LMS), respectively. This is also known as trichromatic colour vision. These colours correspond to the wavelengths of peak light absorption intensities of the modified chromophores (a molecule which absorbs light at a particular wavelength and emits colour as a result). Peak absorptions for L cones are found between 555 and 565 nm, M cones between 530 and 537 nm, and S cones between 415 and 430 nm. Therefore, colour vision results from the peak absorption levels of the shifted cones and, in the end, from the brain's interpretation of the makeup of these wavelength absorption points. The complete process is frequently referred to as the "retinoid cycle."⁽²⁾ (As this is biology related, I won't dive deeper into it on Chem SE.)

Interestingly, ageing processes in the eye cause changes in a person's vision and sensitivity to light during their lifetime. With ageing, the lens's transparency diminishes, particularly for the visible spectrum's short wavelength region (blue light).⁽³⁾

References:

(1) https://science.nasa.gov/ems/09_visiblelight/ 
(2) https://www.ncbi.nlm.nih.gov/books/NBK470227/ 
(3) https://www.bfs.de/EN/topics/opt/visible-light/introduction/introduction.html