Baumkuchen

Calculus Level 3

A baumkuchen or split cake has a hollow unit circular area in the middle with successive ring with the same unit radius, in which the first ring is divided equally in 6 portions, second ring in 12, third ring in 18, and so on, as shown below:

As the ring progresses infinitely, what is the area ratio of the unit circle to each portion of the \(n^{th}\) ring?

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