Solution:
The molar heat capacities are $C_v = \frac{n}{2}R$ and $C_p = C_v + R = \left(\frac{n}{2} + 1\right)R$. Their ratio $\gamma = \frac{C_p}{C_v} = \frac{(\frac{n}{2} + 1)R}{\frac{n}{2}R} = 1 + \frac{2}{n}$.
The ratio of the specific heats $\frac{C_P}{C_V} = \gamma$ in terms of degrees of freedom ($n$) is given by: (2015)
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