Which spectral series of the hydrogen atom are found in the infrared region?

The shortest wavelength in the Lyman series is $912 \ \text{Å}$. Then, the longest wavelength in the series must be (in $\text{Å}$)

The ratio of longest wavelength lines in the Balmer and Paschen series of hydrogen spectrum is

$A$ hydrogen atom transitions from an excited state to the ground state by emitting a photon of wavelength $\lambda$. If $R$ is the Rydberg constant,the principal quantum number $n$ of the excited state is:

$v_{1}$ is the frequency of the series limit of the Lyman series,$v_{2}$ is the frequency of the first line of the Lyman series,and $v_{3}$ is the frequency of the series limit of the Balmer series. Then:

The wavelength of the first spectral line in the Balmer series of a hydrogen atom is $6561 \mathring A$. The wavelength of the second spectral line in the Balmer series of a singly-ionized helium atom is