The ratio of wavelengths of the last line of Balmer series and the first line of Lyman series is

$\mathrm{Wavelength} \mathrm{of} \mathrm{first} \mathrm{line} \mathrm{of} \mathrm{Lymen} \mathrm{series}$

$\frac{1}{{\mathrm{\lambda }}_{\mathrm{L}1}}=\mathrm{k}\left(\frac{1}{1^2}-\frac{1}{2^2}\right)=\frac{3\mathrm{k}}{4}$

$\mathrm{Wavelength} \mathrm{of} \mathrm{the} \mathrm{last} \mathrm{line} \mathrm{of} \mathrm{Balmer}$

$\frac{1}{{\lambda }_{BL}}=k\left(\frac{1}{2^2}-\frac{1}{\propto }\right)=\frac{k}{4}$

$\frac{{\lambda }_{BL}}{{\lambda }_{L1}}=3$