23. The Inter-dimensional Reccurence

Let $V_n$ denote the volume of the unit ball in $\mathbb{R}^n$.

First solve Question 4 to obtain a formula for $V_n$.

Using the formula obtained there, investigate how the volumes of unit balls in different dimensions are related. Derive a recurrence relation between terms of the sequence $(V_n)_{n\geq1}$ and prove that it holds for all applicable dimensions.