O generalizare a unei probleme a lui A. G. Ioachimescu

In this note we study the sequence (s_n )_(n≥1), given by (4). It is shown that (s_n ) is convergent lim┬(n→∞)⁡〖s_n 〗 [-p,1-p] and the order of convergence is given by (5) or (6).
In the particular case p=2, we obtain a problem from the first issue of Gazeta Matematică, in 1895, due to A.G.Ioachimescu, one of founders of this old Romanian magazine.