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 (which 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 sequence.
Original Source Citation
Opuscula analytica, Volume 1, pp. 3-47.
Opera Omnia Citation
Series 1, Volume 15, pp.338-382.