If the series limit frequency of the Lyman series is ν_L, then the series limit frequency of the Pfund series is :

Frequency of emitted photon in a hydrogen atom is given by,

$v=Rc\left(\frac{1}{{n_1}^2}-\frac{1}{{n_2}^2}\right)$

For Lyman series, series limit condition is given by

$n_2=\infty , n_1=1$

$\therefore v_L=Rc\left(\frac{1}{1^2}-\frac{1}{{\infty }^2}\right)=Rc \dots \dots \left(i\right)$

For Pfund series, series limit condition is given by,

$n_2=\infty , n_1=5$

$\therefore v_P=Rc\left(\frac{1}{5^2}-\frac{1}{{\infty }^2}\right)=\frac{Rc}{25} \dots \dots \left(ii\right)$

From equation $\left(i\right)$ and $\left(ii\right)$,

$v_P=\frac{v_L}{25}$