E550 -- De seriebus, in quibus producta ex binis terminis contiguis datam constituunt progressionem

(On series in which the product of two consecutive terms make a given progression)

Given a sequence (what Euler calls a "progression") A, B, C, D, E, F, etc. Euler wants to find another sequence (that Euler calls a "series") a, b, c, d, e, f, etc. such that ab=A, bc=B, cd=C, de=D, ef=E, fg=F, etc. He studies a variety of properties of the second series.

According to the records, it was presented to the St. Petersburg Academy on July 4, 1771.

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