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Wikenigma - an Encyclopedia of Unknowns Wikenigma - an Encyclopedia of the Unknown

The Flint Hills Series

The Flint Hills Series, devised in 2002, by American mathematican Clifford A. Pickover, is a type of 'numerical series' - i.e. the operation of adding infinitely many quantities, one after the other, to a given starting quantity - a.k.a. an infinite summation.

It's expressed as :

$${\displaystyle \sum _{n=1}^{\infty }{\frac {\csc ^{2}n}{n^{3}}}}$$

Many numerical series 'converge' i.e. rise towards a finite number rather than continuing on to infinity. In this case it has not been proved or disproved that convergence occurs.

It is not known if this series converges, since csc2n can have sporadic large values."

Source : Wolfram Mathworld

Note : It has been shown that this question is closely related to the 'irrationality' measure of ฯ€, denoted ฮผ(ฯ€). Ref. Alekseyev, 2011, arXiv.


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