On some properties of patial sums

TL;DR

This paper investigates conditions under which partial sums of rational sequences are neither rational nor algebraic functions, with applications to well-known sequences in analysis and number theory.

Contribution

It provides criteria distinguishing when partial sums of rational sequences are not rational or algebraic functions, advancing understanding in analysis and number theory.

Findings

Criteria for partial sums not being rational functions.

Criteria for partial sums not being algebraic functions.

Application to famous rational sequences in analysis.

Abstract

The paper gives some criteria for partial sums of rational number sequences to be not rational functions and to be not algebraic functions. As an application, we study partial sums of some famous rational number sequences in mathematical analysis with relevance to number theory.