设n为正整数.以2023年天津市高考数学试题最后一题为背景,运用Abel分部求和法及幂级数展开证明了11/12＜lnn!-(n+1/2)lnn+n≤1.这改进了试题所需结论及Rudin在名著《数学分析原理》(Principles of Mathematical Analysis)中给出的结果.
Abstract
Utilizing Abel's summation formula and power series,this paper offers a proof of 11/22＜lnn!-(n+1/2)lnn+n≤1,rooted in the backdrop of the final mathematics question in the 2023 Tianjin college entrance examination.This advancement enhances the conclusion required in the aforementioned test ques-tion,as well as addressing a result featured in Rudin's"Principles of Mathematical Analysis."
关键词
Stirling公式/Abel求和公式/幂级数
Key words
Stirling's formula/Abel's summation formula/power series
维普
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