The reciprocals of tails of the alternating Riemann zeta function

TL;DR

This paper computes the integer parts of reciprocals of tails of the alternating Riemann zeta function at specific points using new inequalities and elementary methods.

Contribution

It introduces novel inequalities and elementary techniques to analyze reciprocals of tails of the alternating Riemann zeta function at specific values.

Findings

Integer parts of reciprocals at s=1,2,3,4 are determined.

New inequalities facilitate tail analysis of the alternating Riemann zeta function.

Elementary methods simplify the computation process.

Abstract

In this paper, we give the integer parts of reciprocals of tails of the alternating Riemann zeta function at $s=1,2,3,4$ by using several new inequalities and elementary method.