The ratio of minimum to maximum wavelength in Balmer series is

$\frac{1}{\lambda}=R\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right] \Rightarrow \frac{\lambda_{\min }}{\lambda_{\max }}=\frac{\left[\frac{1}{2^2}-\frac{1}{3^2}\right]}{\left[\frac{1}{2^2}-\frac{1}{\infty}\right]}=\frac{5}{9}$