2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70327We prove that a certain series defines a constant function using Wolpert's formula for the variation of the length of a geodesic along a Fenchel Nielsen twist. Subsequently we determine the value viewing it as function on the the Deligne Mumford compactification and evaluating it at the stable curve at infinity.January 2004Geometric Topology53A35, 53C65text