On Infinite Series and with Their Some Applications to Euler's Summation Formula

Abstract

Infinite series is still used in engineering, mathematical and physical sciences.In the modern area a great progress is made in the sciences of calculus in addition to what was accompanied by advances in infinite series and their some applications .The aims of this paper is to develop and introduces the infinite series and their some applications to Euler's summation , also we show and explain how to apply the infinite series in Euler's summation .We followed the induction mathematical method and found that : The relationship through the Euler's summation focused on the physical link questioner to make the study as an application for Euler's summation so it can be the beginning of advanced study in concept of the infinite series and their some applications to Euler's summation.