# The three infinite harmonic series and their sums (with topical reference to the Newton and Leibniz series for π)

@article{Soddy1943TheTI,
title={The three infinite harmonic series and their sums (with topical reference to the Newton and Leibniz series for $\pi$)},
author={Frederick Soddy},
journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences},
year={1943},
volume={182},
pages={113 - 129}
}
• F. Soddy
• Published 1943
• Mathematics
• Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
The infinite harmonic series as hitherto understood, whether with alternating or continuous signs, is not the complete series. It may be extended in both directions to infinity, and then it exists in two forms, either with alternating or with continuous signs, both of which have finite sums. These are termed ASD and CSD in contradistinction to the singly infinite harmonic series ASS— or, since the form with alternating signs alone is convergent, SS Examples of both the former and their sums are…

## References

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THIS work is, as we are told in the preface, “the outcome of lectures delivered in the College of Physical Science at Newcastle-upon-Tyne.” It discusses, more fully than is usual in books on algebra,