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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
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3. Bâtineţu-Giurgiu, D. M., Problem 22692, Gaz. Mat. Ser. B 97 (7-8) (1992) p. 287.Google Scholar
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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
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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