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The Balmer series for the H- atom can be observed:

Vidyadip · Accepted Answer

If we measure the frequencies of light emitted due to transitions between excited states and the first excited state.
As a sequence of frequencies with the higher frequencies getting closely packed.
Key concept :
The vatious lines in the atomic spectra are produced when electrons jump fron higher energy state to a lower energy state and photons are emitted.
These spectral lines are called emission lines.

Mainly there are five series and each series is named after its discoverer as Lyman series, Balmer series, Paschan series, Bracket series and Pfund series.
According to the Bohr's theory the wavelength of the radiations emitted from hydrogen atom is given by

$\frac{1}{\lambda}=\text{R}\bigg[\frac{1}{\text{n}_1^2}-\frac{1}{\text{n}_2^2}\bigg]$
$\Rightarrow\ \lambda=\frac{\text{n}_1^2\text{n}_2^2}{(\text{n}_2^2-\text{n}_1^2)\text{R}}=\frac{\text{n}_1^2}{\Big(1-\frac{\text{n}_1^2}{\text{n}_2^2}\Big)\text{R}}$
where $n_2 =$ outer orbit $($electron jumps from this orbit$), n_1 =$ inner orbit $($electron falls in this orbit$)$

First line of the series is called first member, for this lines wavelength is maximum $(\lambda_\text{max})$.
For maximum wavelength if $n_1 = n,$ then $n_2 = n + 1.$
So $\lambda_\text{max}=\frac{\text{n}^2(\text{n}+1)^2}{(2\text{n}+1)\text{R}}$.
Last line of the series is called series limit, for this line wavelength is minimum $(\lambda_\text{max})$.
Foe minimum wavelength $\text{n}_2=\infty,\text{n}_1=\text{n}.\text{ So}\lambda_\text{min}=\frac{\text{n}^2}{\text{R}}.$
The radio of first member and series limit can be calculated as $\frac{\lambda_\text{max}}{\lambda_\text{min}}=\frac{(\text{n}+1)^2}{(2\text{n}+1)}$.

Different spectral series

	Spectral Series	Transition	$\lambda_\text{max}$	$\lambda_\text{min}$	$\frac{\lambda_\text{max}}{\lambda_\text{min}}$	Region
$1.$	Lyman series	$\text{n}_2=2,3,4 \ ....\infty$ $\text{n}_1=1$	$\frac{4}{3\text{R}}$	$\frac{1}{\text{R}}$	$\frac{4}{3}$	Ultraviolet region
$2.$	Blamer series	$\text{n}_2=3,4,5 \ ....\infty$ $\text{n}_1=2$	$\frac{36}{5\text{R}}$	$\frac{4}{\text{R}}$	$\frac{9}{5}$	Visible region
$3.$	Paschen series	$\text{n}_2=4,5,6 \ ....\infty$ $\text{n}_1=3$	$\frac{144}{7\text{R}}$	$\frac{9}{\text{R}}$	$\frac{16}{7}$	Infrared region
$4.$	Bracket series	$\text{n}_2=5,6,7 \ ....\infty$ $\text{n}_1=4$	$\frac{400}{9\text{R}}$	$\frac{16}{\text{R}}$	$\frac{25}{9}$	Infrared region
$5.$	Pfund series	$\text{n}_2=6,7,8 \ ....\infty$ $\text{n}_1=5$	$\frac{900}{11\text{R}}$	$\frac{25}{\text{R}}$	$\frac{36}{11}$	Infrared region

From above discussion we can say Balmer series for the $H-$ atom can be observed if we measure the frequencies of light emitted due to transitions between higher excited states and the first excited state and as a sequence of frequencies with the higher frequencies getting closely packed.

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