The Evaluation of the Sums of More General Series by Bernstein Polynomials

TL;DR

This paper explores the use of Bernstein polynomials to evaluate sums of more general series, extending classical sum evaluations and demonstrating the approach with practical examples.

Contribution

It introduces a novel method using Bernstein polynomials to evaluate complex series sums, expanding the tools available for series analysis.

Findings

Bernstein polynomial approach effectively evaluates general series sums

The method is validated through multiple illustrative examples

Provides a new perspective on series sum evaluation techniques

Abstract

Let n,k be the positive integers, and let S_{k}(n) be the sums of the k-th power of positive integers up to n. By means of that we consider the evaluation of the sum of more general series by Bernstein polynomials. Additionally we show the reality of our idea with some examples.