2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153530We study the asymptotic expansion of the colored Jones polynomial (the Melvin-Morton expansion) using a recursion formula for the deframed universal weight system for the $sl(2)$ Lie algebra. Combined with the formula for the universal weight system for the Lie superalgebra $gl(1|1)$ (which corresponds to the Alexander-Conway knot polynomial) this formula gives a very short proof of the Melvin-Morton conjecture relating the colored Jones invariant and the Alexander-Conway polynomial of knots.20 pages, LaTeX with bezier.styQuantum Algebratext