The Balmer series occurs between the wavelength of $\left[\mathrm{R}=1.0968\times {10}^7{\mathrm{m}}^{-1}\right]$

For Balmer series

$\begin{array}{l}\frac{1}{\mathrm{\lambda }}=\mathrm{R}\left[\frac{1}{2^2}-\frac{1}{{\mathrm{n}}^2}\right]\\ \mathrm{where}\mathrm{n}=3,4,5,.....\mathrm{\infty }\\ \mathrm{To}\mathrm{obtain}\mathrm{the}\mathrm{limits}\mathrm{for}\mathrm{Balmer}\mathrm{series}\mathrm{n}=3\mathrm{and}\mathrm{n}=\mathrm{\infty }\mathrm{respectively}.\\ {\mathrm{\lambda }}_{\max }\left(\mathrm{n}=3\right)=\frac{1}{\mathrm{R}\left[\frac{1}{2^2}-\frac{1}{3^2}\right]}=\frac{36}{5\mathrm{R}}\\ =\frac{36}{5\times 1.0968\times {10}^7}\mathrm{m}=6563{\text{\hspace{0.17em}A}}^{\mathrm{o}}\\ {\mathrm{\lambda }}_{\max }\left(\mathrm{n}=\mathrm{\infty }\right)=\frac{1}{\mathrm{R}\left[\frac{1}{2^2}-\frac{1}{{\mathrm{\infty }}^2}\right]}=\frac{4}{\mathrm{R}}\\ =\frac{4}{1.0968\times {10}^7}\mathrm{m}=3647{\text{\hspace{0.17em}A}}^{\mathrm{o}}\end{array}$