Volume of Unit Hypersphere/Sequence

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Sequence of Volumes of Unit Hyperspheres

The sequence of volumes of the unit sphere in $n$-dimensional space begins as follows:

\(\displaystyle n = 1\) \(:\) \(\displaystyle \map V 1 = 2\)
\(\displaystyle n = 2\) \(:\) \(\displaystyle \map V 2 = 3.1\)
\(\displaystyle n = 3\) \(:\) \(\displaystyle \map V 3 = 4.2\)
\(\displaystyle n = 4\) \(:\) \(\displaystyle \map V 4 = 4.9\)
\(\displaystyle n = 5\) \(:\) \(\displaystyle \map V 5 = 5.264\)
\(\displaystyle n = 6\) \(:\) \(\displaystyle \map V 6 = 5.2\)
\(\displaystyle n = 7\) \(:\) \(\displaystyle \map V 7 = 4.7\)


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