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Series of tetrates:consecutive bases
#1
Just came across an article, which refers to the alternating series



whose terms contain the towers of height 2 of reciprocals of consecutive bases.
The terms of the series in their original notation are



which I converted to



The result is -without explicite derivation, but the method was indicated- given as



Article: Convergence acceleration of series
Pascal Sebah and Xavier Gourdon
http://numbers.computation.free.fr/Const...eration.ps
January 10, 2002


Note: a couple of msgs of mine related to such series you'll find by keyword "tetra-eta-series", which I used earlier
Gottfried Helms, Kassel
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