One student heats hydrogen gas at low pressure and sees a few bright lines.

Hydrogen's lines obey $\tilde{\nu} = R_H\left(\dfrac{1}{n_1^2} - \dfrac{1}{n_2^2}\right)$, with $R_H = 1.097 \times 10^{7}\ \text{m}^{-1}$. Lyman ends on $n_1 = 1$, Balmer on $2$, Paschen on $3$, Brackett on $4$. From level $n$, $\dfrac{n(n - 1)}{2}$ different lines are possible.