(a) For Lyman series
$v_{Lyman} = \frac{c}{\lambda_{\max}} = RO\left\lbrack \frac{1}{(1)^{2}} - \frac{1}{(2)^{2}} \right\rbrack = \frac{3RC}{4}$
For Balmer series
$v_{Balmer} = \frac{c}{\lambda_{\max}} = RO\left\lbrack \frac{1}{(2)^{2}} - \frac{1}{(3)^{2}} \right\rbrack = \frac{5RC}{36}$
$\therefore\frac{v_{Lyman}}{v_{Balmer}} = \frac{27}{5}$