International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 1, Pages 1-6

On the recursive sequence xn+1=1/xn+A/xn1

Stevo Stević

Matematički Fakultet, Studentski Trg 16, Beograd 11000, Serbia and Montenegro

Received 20 July 2000; Revised 8 November 2000

Copyright © 2001 Stevo Stević. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate the periodic character of solutions of the nonlinear difference equation xn+1=1/xn+A/xn1. We give sufficient conditions under which every positive solution of this equation converges to a period two solution. This confirms a conjecture in the work of DeVault et al. (2000).