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Monotonic series for fractions near π and their convergents
Published online by Cambridge University Press: 22 June 2022
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We describe various methods to derive monotonic infinite series for fractions near π and obtain a variety of series for the special case of its convergents. These series immediately show that π is clearly different from these fractions, replicating with series the results in Dalzell [1, 2] and Lucas that used integrals with non-negative integrands to represent the gaps between π and fractions.
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- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/) which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
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- © The Authors, 2022. Published by Cambridge University Press on behalf of The Mathematical Association