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On reciprocal sums of terms of linear recurrences. (English) Zbl 0776.11032
The authors prove an irrationality result for the sum of the infinite series whose terms are reciprocals of a recurrent generated sequence of order \(k\), greater than one and two results for the case \(k=2\). Other related results were proved recently by the reviewer [Acta Arith. 63, 313-323 (1993; Zbl 0770.11036)] and by W. L. McDaniel in a paper to appear in Fibonacci Q.
Reviewer: C.Badea (Orsay)

MSC:
11J72 Irrationality; linear independence over a field
11B37 Recurrences
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References:
[1] ANDRE-JEANIN R.: A note of the irrationality of certain Lucas infinite series. Fibonacci Quart. 29 (1991), 132-136.
[2] BADEA C.: The irrationality of certain infinite series. Glasgow Math. J. 29 (1987), 221-228. · Zbl 0629.10027
[3] BUNDSCHUH P., PETHÖ A.: Zur Transzendenz gewisser Reihen. Monatsh. Math. 104 (1987), 199-223. · Zbl 0601.10025
[4] ERDÖS P., GRAHAM R. L.: Old and new problems and results in combinatorial number theory. Monograph. Enseign. Math. 38, Enseignement Math., Geneva, 1980, pp. 60-66. · Zbl 0434.10001
[5] GOOD I. J.: A reciprocal series of Fibonacci numbers. Fibonacci Quart. 12 (1974), 346. · Zbl 0292.10009
[6] HOGGATT V. E., BICKNELL M. J.: A reciprocal series of Fibonacci numbers with subscripts of 2nk. Fibonacci Quart 14 (1976), 453-455. · Zbl 0356.10005
[7] OPPENHEIM A.: Criteria for irrationality of certain classes of numbers. Amer. Math. Monthly 61 (1954), 235-241. · Zbl 0055.04503
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