Aplicações de sequências e séries de números reais: número de Euler, conjunto de Cantor, sequência de Fibonacci e produto de Wallis.

Abstract

The study of sequences and series of real numbers is of fundamental importance in the study of Differential and Integral Calculus. This work aims to address some applications of sequences and series of real numbers such as: Euler constant showing its irrationality and addressing its relationship with the alternating harmonic series, the Cantor set and its equivalents in R2 (Sierpinski carpet) and R3 (Monger sponge), Fibonacci sequence and its applications in the Pascal triangle and in the Pythagorean triples and the Wallis product with application in the ellipse length. For that, regarding the methodology, bibliographic research was used. Through this work we can conclude that there are several applications of sequences and series of real numbers in many branches of mathematics.