Teorema del binomio y aplicaciones
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Cohecha Torres, Camilo Humberto
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En este trabajo se emplean unas herramientas combinatorias denominadas trayectorias reticulares, para describir las entradas del Triángulo de Pascal y para obtener el Teorema del Binomio. De hecho este teorema y las trayectorias descritas previamente permiten definir los números de Catalan y algunas de sus propiedades. Finalmente se proponen actividades que permitan acercar a los estudiantes a la comprensión y aplicación del Teorema del Binomio.
Abstract. In this work, some combinatorial tools called lattice paths are used in order to define entries in the Pascal's Triangle. Furthermore, a proof of the Binomial Theorem by using lattice paths is described as well, this theorem and lattice paths allow to define Catalan numbers and there are presented some of its properties. Finally, we presented activities to allow students a better understanding of Binomial Theorem and some of its applications.
Abstract. In this work, some combinatorial tools called lattice paths are used in order to define entries in the Pascal's Triangle. Furthermore, a proof of the Binomial Theorem by using lattice paths is described as well, this theorem and lattice paths allow to define Catalan numbers and there are presented some of its properties. Finally, we presented activities to allow students a better understanding of Binomial Theorem and some of its applications.
Abstract
Palabras clave propuestas
Teorema del Binomio; Teorema de Newton; Números de Catalan; Trayectorias reticulares; Conjuntos ordenados; Triángulo de Pascal; Coeficiente binomial; Combinaciones; Binomial Theorem; Theorem of Newton; Catalan numbers; Lattice paths; Ordered sets; Pascal's Triangle; Binomial coefficient; Combinations