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Regarding a generalisation of Ioachimescu's constant

Published online by Cambridge University Press:  23 January 2015

Alina Sîntămărian
Alina Sîntămărian*
Affiliation:
Department of Mathematics, Technical University of Cluj-Napoca, Str. C. Daicoviciu nr. 15, 400020 Cluj-Napoca Romania, e-mail:[email protected]
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Extract

The purpose of this paper is to present some results regarding the limit is of the sequence

In the problem proposed by A. G. Ioachimescu in 1895 [1], 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, problem 3.1, p. 431], [3,4], [5, Theorem 1, parts (a) and (b)], [6, problem P2, parts (i) and (ii)], [7, 8]).

Type
Articles
Information
The Mathematical Gazette , Volume 94 , Issue 530 , July 2010 , pp. 270 - 283
Copyright
Copyright © The Mathematical Association 2010

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References

1. Ioachimescu, A. G., Problem 16, Gaz: Mat. 1 (2) (1895) p. 39.Google Scholar
2. Becheanu, M., Grigore, Gh., Ianus, S., Ichim, I., Probleme de algebra, analiza matematica şi geometrie (Algebra, mathematical analysis and geometry problems), Editura Cartea Romaneâsca, Bucureşti (1991).Google Scholar
3. Bâtineţu-Giurgiu, D. M., Problem 22692, Gaz. Mat. Ser. B 97 (7-8) (1992) p. 287.Google Scholar
4. Bâtineţu-Giurgiu, D. M., Problem C: 1525, Gaz. Mat. Ser. B 99 (4) (1994) p. 191.Google Scholar
5. Bâtineţu-Giurgiu, D. M., Probleme vechi, solutii şi generalizâri noi (Old problems, new generalisations and solutions), Gaz. Mat. Ser. B 100 (5) (1995) pp. 199–206.Google Scholar
6. Berinde, V., Asupra unei probleme a lui A. G. Ioachirnescu (On a A. G. Ioachimescu's problem), Gaz. Mat. Ser. B 99 (7) (1994) pp. 310–313.Google Scholar
7. Acu, D., Asupra unei probleme a lui A. G. Ioachimescu (On a A. G. Ioachimescu's problem), Gaz. Mat. Ser. B 100 (9) (1995) pp. 418–421.Google Scholar
8. Sintâmânan, A., A generalisation of Ioachimescu's constant, Math. Gaz. 93 (November 2009) pp. 456–467.Google Scholar
9. Rizzoli, I., Stolz-Cesáro, O teorernâ (A Stolz-Cesaro theorem), Gaz. Mat. Ser. B 95(10-11-12) (1990) pp. 281–284.Google Scholar
10. Knopp, K., Theory and application of infinite series, Blackie & Son (1951).Google Scholar
11. Bâtineţu-Giurgiu, D. M., Pirşan, L., Radovici-Mârculescu, P., Concursul anual al rezolvitorilor Gazetei Matematice – Piteşti 1994 (partea a doua) (The annual contest of the solvers of Gazeta Matematice – Piteşti 1994 (the second part)), Gaz. Mat. Ser. B 99 (12) (1994) pp. 530–544.Google Scholar