Rational approximation of the finite sum of some sequences

Xu You

doi:10.56754/0719-0646.2701.165

DOI:

https://doi.org/10.56754/0719-0646.2701.165

Abstract

In this paper, we give some rational approximations of \( S(n)=\displaystyle\sum_{j=1}^{n}\frac{1}{n^2+j} \) by the multiple-correction method and present the bounds of its error.

Keywords

Rational approximation , continued fraction , inequalities , multiple-correction method

Mathematics Subject Classification:

40A05 , 40A25 , 41A60 , 26D15

Xu You Department of Mathematics, Beijing Institute of Petrochemical Technology, Beijing 102617, P. R. China. https://orcid.org/0000-0003-2591-5365

Pages: 165–177
Date Published: 2025-04-30
Vol. 27 No. 1 (2025)

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