Rational approximation of the finite sum of some sequences

Xu You

doi:10.56754/0719-0646.2701.165

Authors

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

DOI:

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

Keywords:

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

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.

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