The expression for wavelength is written as $\frac{1}{\lambda}=R Z^2\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$
The last line is a line of shortest wavelength or highest energy. When $n_2=\infty$, we get the last line wavelength.
$\frac{1}{\lambda}=R Z^2\left[\frac{1}{\mathrm{n}_1^2}\right]$
$\lambda_{\text {Series limit }}=\frac{\mathrm{n}_1^2}{\mathrm{RZ}}$
For Lyman series, $\mathrm{n}_1=1$ and for Balmer series $\mathrm{n}_1=2$.
Therefore, $\frac{\lambda_{\text {Lyman }}}{\lambda_{\text {Balmer }}}=\frac{n_{1 \text { Lyman }}^2}{n_{1 \text { Balmer }}^2}=\frac{1^2}{2^2}=\frac{1}{4}=0.25$