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A generalisation of Ioachimescu’s constant

Published online by Cambridge University Press:  01 August 2016

Alina Sȋntămărian
Alina Sȋntămărian*
Affiliation:
Department of Mathematics, Technical University of Cluj-Napoca, Str. C. Daicoviciu nr. 15, 400020 Cluj-Napoca, Romania e-mail: Alina.Sintamarian@math.utcluj.ro
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Extract

In the problem proposed by A. G. Ioachimescu in 1895, it is asked to be shown that the sequence , defined by , for each , is convergent and its limit lies between -2 and -1.

There have been given many generalisations and other results regarding Ioachimescu’s problem in the literature (see, for example, [2], [3], [4, Theorem 1, parts (a) and (b)], [5, problem P2, parts (i) and (ii)],).

Type
Articles
Information
The Mathematical Gazette , Volume 93 , Issue 528 , November 2009 , pp. 456 - 467
Copyright
Copyright © The Mathematical Association 2009

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References

1. Ioachimescu, A. G., Problem 16, Gazeta Matematicá 1 (2), 1895, p. 39.Google Scholar
2. Bătineţu-Giurgiu, D. M., Problem 22692, Gazeta Matematicá, Seria B, 97 (7–8) (1992) p. 287.Google Scholar
3. Bătineţu-Giurgiu, D. M., Problem C: 1525, Gazeta Matematicá, Seria B, 99 (4) (1994) p. 191.Google Scholar
4. Bătineţu-Giurgiu, D. M., Probleme vechi, soluţii şi generalizări noi (Old problems, new generalisations and solutions), Gazeta Matematică, Seria B, 100 (5) (1995) pp. 199–206.Google Scholar
5. Berinde, V., Asupra unei probleme a lui A. G. Ioachimescu (On a problem of A. G. Ioachimescu), Gazeta Matematică, Seria B, 99 (7) (1994) pp. 310–313.Google Scholar
6. Acu, D., Asupra unei problème a lui A. G. Ioachimescu (On a problem of A. G. Ioachimescu), Gazeta Matematică, Seria B, 100 (9) (1995q) pp. 418–421.Google Scholar
7. Rizzoli, I., O teoremă Stolz-Cesàro (A Stolz-Cesàro theorem), Gazeta Matematică, Seria B, 95 (10–11–12) (1990) pp. 281–284.Google Scholar
8. Becheanu, M., Grigore, Gh., Ianuş, S., Ichim, I., Probleme de algebră, analiză matematică şi geometrie (Algebra, mathematical analysis and geometry problems), Editura Cartea Românească, Bucureşti (1991).Google Scholar
9. Knopp, K., Theory and application of infinite series, Blackie & Son (1951).Google Scholar
10. Bătineţu-Giurgiu, D. M., Pîrşan, L., Radovici-Mărculescu, P., Concursul anual al rezolvitorilor Gazetei Matematică - Piteşti 1994 (partea a doua) (The annual contest of the solvers of Gazeta Matematică – Piteşti 1994 (the second part)), Gazeta Matematică, Seria B, 99 (12) (1994) pp. 530–544.Google Scholar