2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144186Let $ p_{i, n}, i=1,..., N(n)=2^{n-1} $ be the lengths of intervals between the neighboring fractions of Brocot sequence $ F_n $. We obtain an asymptotic formula for $σ_β(F_n)=\sum_{i=1}^{N(n)} p_{i, n}^β $,which improves known estimates.36 pagesNumber Theory11B99text