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Fast formulas for slowly convergent alternating series

Published online by Cambridge University Press:  23 January 2015

M.J. Cooker
M.J. Cooker*
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ e-mail: m.cooker@uea.ac.uk
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Extract

One day the Tortoise was discussing with mighty Achilles the behaviour of infinite series. Achilles boasted that his mental powers were so fast that he could exhaust any series summation problem by simply adding up enough terms. But Tortoise was unimpressed:

‘Is that so? What's the sum of this series, then?’ With his tail he drew a line in the sand, and wrote

which is the same as

‘I'll give you until tomorrow to find K to four significant digits!’

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Type
Articles
Information
The Mathematical Gazette , Volume 95 , Issue 533 , July 2011 , pp. 218 - 226
Copyright
Copyright © The Mathematical Association 2012

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References

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