Explanation

(c) Series limit of Balmer series is given by
$\frac{1}{\lambda_{\min}} = R\left( \frac{1}{2^{2}} - \frac{1}{\infty} \right) = \frac{R}{4}$
$R = \frac{4}{\lambda_{\min}} = \frac{4}{6400} = \frac{1}{1600}\mathring{\mathrm{A}}^{- 1}$
Series limit of Paschen series would be
$\frac{1}{\lambda_{\min}} = R\left( \frac{1}{3^{3}} - \frac{1}{\infty} \right) = \frac{R}{9}$
$\lambda_{\min} = \frac{9}{R} = \frac{9}{1/1600} = 14400\mathring{\mathrm{A}}$