To solve this problem, we need to find the ratio of specific heats $\frac{C_P}{C_V} = \gamma$ in terms of degrees of freedom $(n). \\$For an ideal gas, the specific heat capacities at constant volume $(C_V)$ and constant pressure $(C_P)$ are related to the degrees of freedom $(n)$ as follows:$\\ C_V = \frac{n}{2} R \\ C_P = C_V + R = \frac{n}{2} R + R = \left(\frac{n}{2} + 1\right) R \\$The ratio of specific heats $\gamma$ is given by:$\\ \gamma = \frac{C_P}{C_V} = \frac{\left(\frac{n}{2} + 1\right) R}{\frac{n}{2} R} \\$Simplifying the expression:$\\ \gamma = \frac{\frac{n}{2} + 1}{\frac{n}{2}} \\ \gamma = \frac{n + 2}{n} \\$This can be rewritten as:$\\ \gamma = 1 + \frac{2}{n} \\$Therefore, the correct option is Option 2: $1 + \frac{2}{n} \\$This corresponds to the given correct option.