In a hydrogen atom the electron makes a transition from (n + 1) ^...

${E}_{n} = - \dfrac{Rhc}{{n}^{2}}$
${E}_{n + 1} = - \dfrac{Rhc}{( n + 1{)}^{2}}$
$\DeltaE = {E}_{n + 1} - {E}_{n}$
$hv = Rhc \left[\dfrac{1}{{n}^{2}} - \dfrac{1}{( n + 1{)}^{2}}\right]$
$v = R . c\left[\dfrac{{\left(n + 1\right)}^{2} - {n}^{2}}{{n}^{2}{\left(n + 1\right)}^{2}}\right]$
$v = R . c\left[\dfrac{1 + 2n}{{n}^{2}{\left(n + 1\right)}^{2}}\right]$

$n > > 1 ⇒$$v = R . c\left[\dfrac{2n}{{n}^{2} \times {n}^{2}}\right] = \dfrac{2RC}{{n}^{3}}$

$v \infty \dfrac{1}{{n}^{3}}$