exercise:E6f17799c6

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Let [math]\Bbar_1(0)[/math] denote the unit ball of [math]\mathbb{R}^d[/math].

• Use Lemma to compute [math]\lambda^d(\Bbar_1(0))[/math] for [math]d=1,\dots,10[/math].
• Compute [math]\lim_{d\rightarrow\infty}\lambda^d(\Bbar_1(0))[/math].
• Show that [math]\lambda^d(\Bbar_1(0))=\medfrac{\pi^{d/2}}{\Gamma(d/2+1)}[/math] holds, where [math]\Gamma\colon(0,\infty)\rightarrow\mathbb{R}[/math] denotes the Gamma function.