The ratio of the largest to shortest wavelengths in Lyman series of hydrogen spectra is :

$\frac{4}{3}$

For Lyman series $\frac{1}{\lambda_{\max }}=R\left[\frac{1}{1^2}-\frac{1}{2^2}\right]=\frac{3}{4} R$

and  $\frac{1}{\lambda_{\min }}=R\left[\frac{1}{1^2}-\frac{1}{\infty^2}\right]=\frac{R}{1} \Rightarrow \frac{\lambda_{\max }}{\lambda_{\min }}=\frac{4}{3}$