In a hydrogen like atom electron make transition from an energy level with quantum number $$n$$ to another with quantum number $$\left( {n - 1} \right).$$  If $$n>>1,$$   the frequency of radiation emitted is proportional to :

Solution :
$$\eqalign{ & \Delta E = hv \cr & v = \frac{{\Delta E}}{h} = k\left[ {\frac{1}{{{{\left( {n - 1} \right)}^2}}} - \frac{1}{{{n^2}}}} \right] = \frac{{k\left( {2n - 1} \right)}}{{{n^2}{{\left( {n - 1} \right)}^2}}} \cr & \approx \frac{{2k}}{{{n^3}}}\,\,{\text{or,}}\,\,v \propto \frac{1}{{{n^3}}} \cr} $$